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SCMUUL OF KUUCATIOIN
LIBRARY
TEXTBOOK COLLECTION
GIFT OF
THE PUBLISHERS
STANFORD N^^ U N' I V E R S I TY
LIBRARIES
DF.'P'^RrMF' T OF
F.DLK>ATfOM
*i
t>-i»'
APR 1 1009
LELANU S I AN rUHT)
JUNIOR LTNIVFRSITY )
(
MENTAL ARITHMETIC
BT
G. A. WENTWORTH, A.M.
▲UTHOB OF A SBBIE8 OF TBXT-BOOKS IN MATHBMATICS
BOSTON, U.S.A.
PUBLISHED BY GINN & COMPANY
1895
e
A/"
615117
C
Entered according to Act of CongreM, tn tbe year 1896. by
G. A. WENTWOBTH,
in the OlHoe of tbe Librarian of Congreu, at WaahlDgton.
MENTAL AEITHMETIC.
CHAPTER I.
INTEGRAL NUMBERS.
LesBon 1.
1. Mary has 2 cents, and her mother gives her 1
more; how many cents has Mary then ?
2. Charles had 2 marbles, and found 2 more in the
schoolyard ; how many marbles had he then ?
3. Lucy found 3 eggs in a box and 3 more in the
hay ; how many eggs did she find in all ?
4. John gave 3 pond-lilies to Hattie, and Arthur
gave her 4; how many had she in all ?
5. A boy has 5 rabbits in one pen and 2 in an-
other ; how many rabbits has he in both pens ?
6. Mr. Brown had 4 horses, and bought 3 more;
how many horses had he then?
7. Agnes has 4 spools of black thread and 6 spools
of white; how many spools has she of both kinds?
8. James earned 6 dollars and afterwards 4 dollars
more ; how many dollars did he earn ?
9. Mrs. Adams paid her grocer 5 dollars for sugar
and 3 dollars for flour ; how many dollars did she pay?
2 MENTAL ABITHMETIO.
LeMon 2.
1. Charles spent 7 cents for oranges and 3 cents
for apples ; how many cents did he spend in all ?
2. Anna has 6 red roses and 2 white roses ; how
many roses has she ?
3. If there are 3 birds on one tree and 4 on an-
other, how many birds are there on both trees ?
4. A boy gets 2 stamps from his sister and 5 from
his mother ; how many stamps has he then ?
5. If a man has 4 bay horses and 6 white horses,
how many horses has he ?
6. I can see 5 dogs in the street and 3 in the yard ;
how many dogs can I see ?
7. If one boy makes 3 snow-men and another makes
6, how many snow-men do both boys make ?
8. There are 2 boys and 7 girls in the front row ;
how many children are there in the front row ?
9. I have 4 books on my table and 4 on the shelf ;
how many books have I ?
10. A farmer has 3 cords of wood in one pile and
6 cords in another ; how many cords has he ?
11. If 6 inches of snow fall in the forenoon and 4
in the afternoon, how many inches fall in the day ?
12. If a school has 2 men and 8 women for teach-
ers, how many teachers are there in the school ?
13. There were 3 boys in the class, and 6 more
entered ; how many boys were there then ?
14. One of my book-cases has 4 shelves and an-
other has 5 ; how many shelves have both ?
15. A boy spent 5 cents for an orange and 5 cents
for three apples ; how many cents did he spend ?
MENTAL ARITHMETIC. 3
LoBson 3.
ADDITION TABLE.
1111111111
0123456789
2
2
2
2
2
2
2
2
2
2
1
2
3
4
5
6
7
8
9
3
3
3
3
3
3
, 3
3
3
3
1
2
3
4
6
6
7
8
9
4
4
4
4
4
4
4
4
4
4
1
2
3
4
5
6
7
8
9
5
6
5
5
5
6
6
6
6
5
1
2
3
4
5
6
7
8
9
6
6
6
6
6
6
6
6
6
6
1
2
3
4
5
6
7
8
9
7
7
7
7
7
7
7
7
7
7
1
2
3
4
6
6
7
8
9
8
8
8
8
8
8
8
8
8
8
1
2
3
4
5
6
7
8
9
9
9
9
9
9
9
9
9
9
9
1
2
3
4
5
6
7
8
9
Note. The Teacher should copy this Addition Table on the
board, and require each pupU in turn to name the sums as the
pointer touches the examples at random. The drill should be
continued daily until every pupil is absolutely certain of the
required answer.
4 MENTAL ABITHMBTIC.
ZaeajBon 4.
1. Maude picked 3 white roses and 8 red ones;
how many roses did she pick ?
2. Henry spent 7 cents for oranges and 5 cents for
apples ; how many cents did he spend ?
3. I have 4 pears in one basket and 9 in another ;
how many pears have I ?
4. If I pay my grocer 9 dollars for flour and 3
dollars for sugar, how many dollars do I pay him ?
5. A man has 8 dollars in bills and 5 dollars in
silver ; how many dollars has he ?
6. How many trees are there in an orchard which
has 9 apple trees and 6 pear trees ?
7. There are 7 desks in one row and 6 in another ;
how many desks are there in both rows ?
8. A peddler sells 8 knives at one house and 7 at
another ; how many knives does he sell ?
9. A man pays 9 dollars for boots and 4 dollars for
a hat ; how many dollars does he pay for both ?
10. A girl pays 10 cents for worsted and 8 cents
for thread ; how many cents does she pay for both ?
11. A farmer has 3 cows in the stable and 16 in
the yard ; how many cows has he in all ?
12. In a livery stable there are 12 black horses and
6 white horses ; how many are there in the stable ?
13. Henry found 6 eggs in one nest and 13 in an-
other ; how many eggs did he find in both nests ?
14. One child has 11 cents and another has 7 ;
how many cents have both children ?
15. John is 9 years old and Mary is 8 years older ;
how old is Mary ?
MEirrjLL ASITHKETia 5
5.
1. A boy fiaw 7 crows on the ground and 9 flying
about ; bow many crowB did be see ?
2. One ben bae 9 chickens and another has 8 ; bow
many chickens have both hens ?
3. John paid 7 cents for his block of paper and
William paid 13 cents for his ; how many cents did
both blocks cost ?
4. If I pay 12 cents for postage on one bundle and
8 cents -on another, how many cents do I pay ?
5. Lucy bought 11 yards of white ribbon and 6
yards of red ; how many yards did she buy ?
6. Mary is 9 years old and her brother is 10^
what is the sum of their ages ?
7. The. cook used 6 eggs for a pudding and 9 for
cake ; how many eggs did she nse in all ?
8. A farmer sold 9 bushelfi of potatoes to one man
and 9 to another ; how many bushels did he sell ?
9. If there are 7 apples in one dish and 9 in an-
other, how many apples are there in both dishes ?
UO. I paid 7 dollars for a ton of coal and 6 dolloES
for a cord of wood ; how many dollars did I pay ?
U. A boy has 8 cents and earns 8 cents more;
how many oente has he then ?
12. I walked 6 miles and rode 14 miles; how
many miles did I go ?
13. If I pay 12 cents for paper and 6 cents lor
pencils, how many cents do I spend ?
14. A farmer has 8 Jersey cows and 7 Xhnhaan
cows ; liow many cows bas he in all ?
15. How many eggs are 8 egp and 9 eggs ?
6 MENTAL ABITHMETIC.
LesBon 6.
1. A farmer sold 8 sheep and 6 lambs ; how many
sheep and lambs did he sell ?
2. My father paid 12 dollars for a coat and 5 dol-
lars for boots ; how many dollars did he pay for both ?
3. If in one class there are 7 scholars and in
another 9, how many are there in both classes ?
4. One roll of ribbon contains 8 yards and another
9 ; how many yards do both rpUs contain ?
5. George caught 6 trout and John caught 12 ;
how many did both boys catch ?
6. A boy picked 8 quarts of berries in the fore-
noon and 7 quarts in the afternoon ; how many quarts
did he pick in the day ?
7. A girl bought a quire of paper for 12 cents and
a bunch of envelopes for 7 ; how many cents did she
pay for paper and envelopes ?
8. One shelf has 7 books and another has 11 ; how
many books are there on both shelves ?
9. One string is 9 inches long, another is 6 inches
long ; how many inches are there in both strings ?
10. If I put 7 eggs with 9 eggs, how many eggs
shall I have ?
11. Florence had 6 white roses and 8 red roses ;
how many roses had she in all ?
12. Charles paid 5 cents for car fare and 14 cents
for peaches ; how many cents did he spend ?
13. One girl hemmed 7 handkerchiefs and another
hemmed 6 ; how many did both girls hem ?
14. One piece of cloth contains 8 yards and another
contains 7 yards ; how many yards in both pieces ?
MENTAL ARITHMETIC. 7
Lesson 7.
1. How many are 1 and 6 ? 11 and 6 ? 21 and 6 ?
31 and 6 ? 41 and 6 ? 51 and 6 ? 61 and 6 ? 71
and 6 ? 81 and 6 ? 91 and 6 ?
2. How many are 2 and 6 ? 12 and 6 ? 22 and 6 ?
32 and 6 ? 42 and 6 ? 52 and 6 ? 62 and 6 ? 72
and 6 ? 82 and 6 ? 92 and 6 ?
3. How many are 3 and 6 ? 13 and 6 ? 23 and 6 ?
33 and 6 ? 43 and 6 ? 53 and 6 ? 63 and 6 ? 73
and 6 ? 83 and 6 ? 93 and 6 ?
4. How many are 4 and 6 ? 14 and 6 ? 24 and 6 ?
34 and 6 ? 44 and 6 ? 54 and 6 ? 64 and 6 ? 74
and 6? 84 and 6? 94 and 6 ?
5. How many are 5 and 6 ? 15 and 6 ? 25 and 6 ?
36 and 6 ? 45 and 6 ? 55 and 6 ? 65 and 6 ? 76
and 6 ? S5 and 6 ? 95 and 6 ?
6. How many are 6 and 6 ? 16 and 6 ? 26 and 6 ?
36 and 6 ? 46 and 6 ? 56 and 6 ? 66 and 6 ? 76
and 6? 86 and 6? 96 and 6?
7. How many are 7 and 6 ? 17 and 6 ? 27 and 6 ?
37 and 6 ? 47 and 6 ? 57 and 6 ? 67 and 6 ? 77
and 6 ? 87 and 6 ? 97 and 6 ?
8. How many are 8 and 6 ? 18 and 6 ? 28 and 6 ?
38 and 6 ? 48 and 6 ? 58 and 6 ? 68 and 6 ? 78
and 6? 88 and 6? 98 and 6 ?
9. How many are 9 and 6 ? 19 and 6 ? 29 and 6 ?
39 and 6 ? 49 and 6 ? 59 and 6 ? 69 and 6 ? 79
and 6 ? 89 and 6 ? 99 and 6 ?
10. How many are 10 and 6 ? 20 and 6 ? 30 and
6 ? 40 and 6 ? 50 and 6 ? 60 and 6 ? 70 and 6 ?
80 and 6 ? 90 and 6 ?
8 MENTAL ARITHMETIC.
LesBon 8.
1. How many are 1 and 7 ? 11 and 7 ? 21 and 7 ?
31 and 7 ? 41 and 7 ? 51 and 7 ? 61 and 7 ? 71
and 7 ? 81 and 7 ? 91 and 7 ?
2. How many are 2 and 7 ? 12 and 7 ? 22 and 7 ?
32 and 7 ? 42 and 7? 52 and 7 ? 62 and 7 ? 72
and 7? 82 and 7 ? 92 and 7?
3. How many are 3 and 7 ? 13 and 7 ? 23 and 7 ?
33 and 7 ? 43 and 7 ? 53 and 7 ? 63 and 7 ? 73
and 7 ? 83 and 7 ? 93 and 7 ?
4. How many are 4 and 7 ? 14 and 7 ? 24 and 7 ?
34 and 7 ? 44 and 7 ? 54 and 7 ? 64 and 7 ? 74
and 7 ? 84 and 7 ? 94 and 7 ?
5. How many are 5 and 7 ? 15 and 7 ? 25 and 7 ?
35 and 7 ? 45 and 7 ? 55 and 7 ? 65 and 7 ? 75
and 7 ? 85 and 7 ? 95 and 7 ?
6. How many are 6 and 7 ? 16 and 7 ? 26 and 7 ?
36 and 7 ? 46 and 7 ? 56 and 7 ? 66 and 7 ? 76
and 7 ? 86 and 7 ? 96 and 7 ?
7. How many are 7 and 7 ? 17 and 7 ? 27 and 7 ?
37 and 7? 47 and 7? 57 and 7 ? 67 and 7? 77
and 7 ? 87 and 7 ? 97 an^ 7 ?
8. How many are 8 and 7 ? 18 and 7 ? 28 and 7 ?
38 and 7 ? 48 and 7 ? 58 and 7 ? 68 and 7 ? 78
and 7 ? 88 and 7 ? 98 and 7 ?
9. How many are 9 and 7 ? 19 and 7 ? 29 and 7 ?
39 and 7 ? 49 and 7 ? 59 and 7 ? 69 and 7 ? 79
and 7 ? 89 and 7 ? 99 and 7 ?
10. How many are 10 and 7 ? 20 and 7 ? 30 and
7 ? 40 and 7 ? 50 and 7 ? .60 and 7 ? 70 and 7 ?
80 and 7? 90 and 7 ?
MENTAL ARITHMETIC. 9
LOBBOn 9.
1. How many are 1 and 8 ? 11 and 8 ? 21 and 8 ?
31 and 8 ? 41 and 8 ? 51 and 8 ? 61 and 8 ? 71
and 8 ? 81 and 8 ? 91 and 8 ?
2. How mahy are 2 and 8 ? 12 and 8 ? 22 and 8 ?
32 and 8 ? 42 and 8 ? 52 and 8 ? 62 and 8 ? 72
and 8 ? 82 and 8 ? 92 and 8 ?
3. How many are 3 and 8 ? 13 and 8 ? 23 and 8 ?
33 and 8 ? 43 and 8 ? 53 and 8 ? 63 and 8 ? 73
and 8? 83 and 8? 93 and 8 ?
4. How many are 4 and 8 ? 14 and 8 ? 24 and 8 ?
34 and 8 ? 44 and 8 ? 54 and 8 ? 64 and 8 ? 74
and 8? 84 and 8 ? 94 and 8?
5. How many are 5 and 8 ? 16 and 8 ? 25 and 8 ?
35 and 8 ? 45 and 8 ? 55 and 8 ? 65 and 8 ? 76
and 8? 85 and 8? 95 and 8?
6. How many are 6 and 8 ? 16 and 8 ? 26 and 8 ?
36 and 8? 46 and 8? 56 and 8? 66 and 8? 76
and 8 ? 86 and 8 ? 96 and 8 ?
7. How many are 7 and 8 ? 17 and 8 ? 27 and 8 ?
37 and 8? 47 and 8? 57 and 8? 67 and 8? 77
and 8 ? 87 and 8 ? 97 and 8 ?
8. How many are 8 and 8 ? 18 and 8 ? 28 and 8 ?
38 and 8 ? 48 and 8 ? 58 and 8 ? 68 and 8 ? 78
and 8? 88 and 8? 98 and 8?
9. How many are 9 and 8 ? 19 and 8 ? 29 and 8 ?
39 and 8 ? 49 and 8 ? 59 and 8 ? 69 and 8 ? 79
and 8 ? 89 and 8 ? 99 and 8 ?
10. How many are 10 and 8 ? 20 and 8 ? 30 and
8 ? 40 and 8 ? 50 and 8 ? 60 and 8 ? 70 and 8 ?
80 and 8 ? 90 and 8 ?
10 MENTAL ARITHMETIC.
Lesson 10.
1. How many are 1 and 9 ? 11 and 9 ? 21 and 9?
31 and 9 ? 41 and 9 ? 51 and 9 ? 61 and 9 ? 71 and
9 ? 81 and 9 ? 91 and 9 ?
2. How many are 2 and9? 12 and 9? 22 and 9?
32 and 9? 42 and 9? 52 and 9? 62 and 9? 72
and 9 ? 82 and 9 ? 92 and 9 ?
3. How many are 3 and 9 ? 13 and 9 ? 23 and 9 ?
33 and 9? 43 and 9? 53 and 9? 63 and 9? 73
and 9 ? 83 and 9? 93 and 9?
4. How many are 4 and 9? 14and9? 24 and9?
34 and 9 ? 44 and 9 ? 54 and 9? 64 and 9 ? 74
and 9? 84 and 9 ? 94 and 9?
5. How many are 5 and 9 ? 15 and 9 ? 25 and 9 ?
35 and 9? 45 and 9? 55 and 9? 65 and 9? 75
and 9? 85 and 9? 95 and 9?
6. How many are 6 and 9 ? 16 and 9 ? 26 and 9 ?
36 and 9? 46 and 9? 56 and 9? 66 and 9? 76
and 9? 86 and 9? 96 and 9?
7. How many are 7 and 9 ? 17 and 9 ? 27 and 9 ?
37 and 9 ? 47 and 9 ? 57 and 9 ? 67 and 9 ? 77
and 9? 87 and 9? 97 and 9?
8. How many are 8 and 9 ? 18and9? 28and9?
38 and 9? 48 and 9? 58 and 9? 68 and 9? 78
and 9? 88 and 9? 98 and 9 ?
9. How many are 9 and 9 ? 19and9? 29and9?
39 and 9? 49 and 9? 59 and 9? 69 and 9? 79
and 9? 89 and 9? 99 and 9?
10. How many are 10 and 9 ? 20 and 9 ? 30 and
9? 40 and 9? 50 and 9? 60 and 9 ? 70 and 9? 80
and 9 ? 90 and 9? 90 and 10 ?
MENTAL ARITHMETIC. 11
laesBon 11.
1. How many are 13 and 8 ? 15and7? 14and9?
16 and 6? 18 and 5? 17 and 8? 19 and 7 ? 12 and
9? 18 and 9? 17 and 6?
2. Howinanyare21and9? 25 and 6? 23 and 8?
26 and 7? 28 and 9? 25 and 7? 24 and 7? 27 and
9? 26 and 8? 23 and 9?
3. How many are 33 and 9 ? 36 and 8? 32 and 9?
37 and 6? 39 and 6 ? 36 and 9? 35 and 6? 34 and
8? 38 and 7? 37 and 9?
4. How many are 42 and 8 ? 47 and 4? 49 and 5?
43 and 7? 45 and 8? 48 and 6? 46 and 7 ? 47 and
7? 44 and 9? 48 and 8?
5. How many are 54 and 8 ? 52 and 9? 57 and 6?
53 and 7? 58 and 5? 56 and 8? 54 and 8? 55 and
7? 59 and 9? 58 and 7?
6. How many are 66 and 9 ? 69 and 6? 64 and 8?
68 and 6? 65 and 8? 63 and 9? 67 and 8? 66 and
8? 69 and 3? 68 and 5?
7. How many are 75 and 6 ? 74 and 9? 79 and 4?
77 and 6? 75 and 9 ? 73 and 9 ? 78 and 5? 76 and
7? 78 and 9? 75 and 7?
8. How many are 82 and 9 ? 85 and 6? 89 and 9?
86 and 7? 87 and 4? 85 and 7? 84 and 8? 83 and
7? 86 and 6? 87 and 9?
9. How many are 68 and 8 ? 76and5? 47and6?
28 and 4? 35 and 8? 24 and 9 ? 56 and 4? 57 and
9? 65 and 7? 69 and 4?
10. How many are 84 and 7? 87 and 3? 88 and
9? 79 and 6? 88 and 8? 79 and 9? 33 and 7? 46
and 8? 57 and 7? 64 and 9?
12 MENTAL ABITUMETIC.
Leason 12.
■
1. Tom has 8 marbles in one pocket and 13 in
another ; how many marbles has he in both pockets ?
2. How many dollars must I pay for a coat worth
21 dollars and trousers worth 9 dollars ?
3. Frank planted 33 rows of com, and Edward
only 9 rows ; how many rows did both boys plant ?
4. One of my bundles weighs 15 pounds, and the
other 7 pounds ; how many pounds do both weigh ?
5. A man pays 42 dollars for a suit of clothes for
himself and 8 dollars for a suit for a boy ; how many
dollars does he pay for both suits ?
6. There are 35 pounds of nails in a keg and 8
pounds in a box ; how many pounds in all ?
7. One family uses 28 quarts of milk in a week,
another 9 quarts ; how many quarts do both use ?
8. Irving had 39 cents and received 6 cents more ;
how many cents had he then ?
9. There are 56 words on one page and only 8 on
another ; how many words are there on both pages ?
10. A grocer sold 35 pounds of sugar and 6 pounds
of coffee ; how many pounds of sugar and coffee did
he sell ?
11. Mary takes 9 stitches in a minute, while her
mother takes 28 ; how many stitches do both take in
a minute ?
12. In my fence there are 9 posts and 33 rails ;
how many posts and rails are there ?
13. There are 7 days in one week and 84 days in
twelve weeks ; how many days are there in thirteen
weeks?
MENTAL ABITHMBTIG. 13
Lesson 13.
1. I put 7 potatoes into a basket that had 46 pota-
toes ; how many potatoes were in the basket then ?
2. How many scholars are there in a school of 52
girls and 9 boys ?
3. I saw 68 cows and 8 horses ; how many animals
did I see ?
4. A boy counted 79 flies and 6 hornets ; how many
insects did he count ?
5. A farmer has 33 apple trees and 7 pear trees ;
how many trees of both kinds has he ?
6. John has 69 hens and 6 ducks ; how many fowls
has he ?
7. A woman knits 48 mittens and 8 gloves ; how
many mittens and gloves does she knit ?
8. Maud gathered 36 pansies and 9 roses ; how
many flowers did she gather ?
9. There are 24 chairs and 9 tables in the build-
ing ; how many chairs and tables together are there ?
10. I have 73 books and 9 pamphlets ; how many
books and pamphlets together have I ?
11. One piece of ice weighs 47 pounds, another
6 pounds ; how many pounds do both pieces weigh ?
'12. One tree bore 85 oranges, another bore only 7 ;
how many oranges did both trees bear ?
13. I read 89 pages before dinner and 9 pages after
dinner ; how many pages did I read in all ?
14. There are 84 apples on the ground ; how many
will there be when 8 more have fallen ?
15. I had 86 cents and found 9 more ; how many
cents had I then ?
14 MENTAL ARITHMETIC.
Lesson 14.
1. A merchant travels 6 miles by stage, 5 miles by
rail, and 4 miles by boat ; how many miles does he
travel ?
2. A butcher sells 8 pounds of steak to one family,
5 pounds to another, and 6 pounds to another ; how
many pounds does he sell to the three families ?
3. How many quarts of blackberries are picked by
a boy who brings home 4 quarts on Monday, 3 quarts
on Tuesday, and 6 quarts on Wednesday ?
4. A lady spent 3 dollars for gloves, 5 dollars for
boots, and 7 dollars for a hat ; how many dollars did
she pay for all ?
5. A milkman has 8 quarts of milk in one can, 5
quarts in another, and 6 quarts in another ; how many
quarts has he in the three cans ?
6. A grocer put up 11 pounds of sugar, 5 pounds
of coffee, and 3 pounds of butter ; how many pounds
did all weigh ?
7. Arthur has in his collection 8 butterflies, 7
moths, and 4 beetles ; how many insects has he in all ?
8. How many trees are there in a street where 7
oaks, 6 maples, and 5 elms are planted ?
9. A lawyer collected 7 dollars from one man, 5
dollars from another, and 6 dollars from another ;
how many dollars did he collect from the three men ?
10. A gardener picked 7 quarts of strawberries
from one bed, 8 quarts from another, and 6 quarts
from another ; how many quarts did he pick ?
11. A drover bought 14 sheep, 7 cows, and 4 pigs;
how many animals did he buy ?
MBKTAL ABITHMETIO. 16
XieMon 15.
1. James dug 8 bushels of potatoes, Frank 5 bosh-
els, and Henry 9 bushels ; how many bushels did the
three boys dig ?
2. Sarah paid 8 cents for pins, 4 cents for thread,
and 9 for needles ; how many cents did she spend ?
3. From a nest of eggs George gave 7 to his mother,
5 to his aunt, and 3 to a poor woman ; how many
eggs did he find ?
4. On a telegraph-pole there are 9 wires on the
lower cross-piece, 7 on the middle one, and 5 on the
upper one ; how many wires are there on the pole ?
5. A liveryman has an omnibus carrying 12 per-
sons, a hack carrying 6, and a cab carrying 3 ; how
many persons will the three carry ?
6. Walter goes to the post-office with 10 cents for
car fare, 8 cents for postage, and 5 cents besides ;
how many cents has he in all ?
7. Helen spent 6 cents, Grace 7, and Annie 9 ; how
many cents did the three girls spo^id ?
8. A farmer sold 15 bushels of potatoes, 4 of
onions, and 3 of turnips ; how many bushels of vege-
tables did he sell ?
9. If there are 12 books on one shelf, 7 on another,
and 5 on another, how many books are there in all ?
10. An agent sold an album for 5 dollars, a Bible
for 9 dollars, and a history for 8 dollars ; how many
dollars did he receive for the three books ?
11. A woman puts up 11 cans of peaches, 12 of
raspberries, and 5 of cherries ; how many cans does
she put up ?
16 MENTAL ARITHMETIC.
Leaaon 16.
jL It is 3 feet from the ground to tlie sills of a
house, 16 feet from the sills to the eaves, and the
ridgepole is 8 feet above the eaves ; how many feet
from the ground is the ridgepole ?
2. A stovepipe has two bends. The first straight
piece is 8 feet, the second 14 feet, and the third 9
feet ; how many feet are there in the stovepipe ?
3. A man pays 18 dollars for a coat, 8 dollars for
trousers, and 4 dollars for a vest ; how many dollars
does he pay for the suit ?
4. A sled is worth 5 dollars, a gun 11 dollars, and
a boat 20 dollars ; what is the value of the three ?
5. There are 17 gallons of oil in one can, 10 gal-
lons in another, and 8 gallons in another; how many
gallons are there in all ?
6. One granite block is 12 feet high, another is
9 feet, and another is 7 feet ; how high a monument
can be made by the three blocks ?
7. A farmer has 15 acres under cultivation, 10
acres in woodland, and 9 acres in pasture ; how many
acres are there in his farm ?
8. A milkman has 13 red cows, 8 black ones, and
7 black and white ; how many cows has he in all ?
9. If I owe my grocer 12 dollars, my butcher 7
dollars, and my baker 6 dollars, how many dollars
do I owe the three together?
10. In a certain book 12 pages are given to addi-
tion, 10 pages to subtraction, and 12 pages to multi-
plication ; how many pages are given to the three
processes ?
MENTAL ABITHMBTIO. 17
Leaaoa 17.
SUBTRACTION TAB£B
1
2
3
4
5
6
7
8
9
10
-1
—1
-1
—1
-1
—1
-1
-1
—1
-1
2
3
4
6
6
7
8
9
10
11
-2
—2
—2
-2
-2
-2
—2
—2
-2
—2
3
4
5
6
7
8
9.
10
11
12
—3
—3
—3
—3
—3
-3
T-B-y
-3
—3
-3
4
5
6
7
8
9
10
11
12
13
—4
—4
—4
-4
—4
—4
—4
-4
—4
-4
5
6
7
8
9
10
11
12
13
14
-6
-6
-6
-5
-5
-6
-5
—6
-6
—5
6
7
8
9
10
11
12
13
14
16
-6
-6
-6
-6
-6
-6
-6
-6
-6
-6
7
8
9
10
11
12
13
14
15
16
—7
—7
—7
-7
-7
—7
—7
-7
-7
-7
8
9
10
11
12
13
14
16
16
17
-8
-8
-8
-8
-8
-8
-8
-8
-8
-8
9
10
11
12
13
14
16
16
17
18
—9
-9
-9
-9
-9
-9
-9
-9
-9
-9
Note. The Teacher should copy this Subtraction Table on
the board, and require each pupil in turn to name the differ-
ences as the pointer touches the examples at random. The
drill should be continued daily until every pupil is absolutely
certain of the required answer,
18 MENTAL ABITHMETIG.
1. William had 3 slate pencils^ but gave 1 to his
brother ; how many had he left ?
2. Kate had 5 cents, but spent 2 cents for a lead-
pencil ; how many cents had she left ?
3. Sarah had 5 rose-bushes, but 3 of them were
killed by the frost ; how many remained ?
4. I found 6 eggs, but 3 of them were bad ; how
maiiy were good ?
5. A flock of 7 wild ducks were swimming in a
pond ; a man shot 2 of them, the rest flew away ; how
many flew away ?
6. Mr. Shaw had 8 cows. After he had sold 5 of
them, how many did he have ?
7. There were 9 trees in front of Mr. Hall's house.
After 4 were cut down, how many remained ?
8. Harry received 10 cents for picking the stones
off the lawn, but had to pay his brother 4 cents for
helping him ; how many cents had Harry left ?
9. Henry's mother gave him 11 cents ; after spend-
ing 2 cents for a top, how many has he left ?•
10. A hen had 12 chickens until a hawk killed 4
of them ; how many were left ?
11. Gertrude had 9 pansies, but gave 3 to her
teacher ; how many had she then ?
12. There were 11 birds in a tree, but a boy fright-
ened away 4 ; how many were left ?
13. Frank had 8 apples, and gave 3 to Fred; how
many had Frank then ?
14. Two boys earned 10 cents ; one of them earned
3 ; how many did the other earn ?
MENTAL ABITHMBTIG. 19
IiesBon 19.
1. Lewis picked 13 quarts of berries, 4 quarts more
than Frank picked ; how many quarts did Frank pick ?
2. Mrs. Jones puts up 11 cans of berries ; 5 cans
are raspberries and the rest blueberries ; how many
cans of blueberries are there ?
3. Mary is 14 3nears old ; her brother is 5 years
younger ; how old is her brother ?
4. One monument is 12 feet high, another is 8
feet ; how many feet higher is one than the other ?
5. A grocer sells 4 gallons of vinegar from a keg
containing 10 gallons ; how many gallons are left ?
6. In a flock of 12 ducks and geese there are 5
geese ; how many ducks are there ?
7. A man having 15 dollars pays 8 dollars for a
railroad ticket ; how many dollars has he left ?
8. It is 4 miles from Boston to Chelsea, and 11
miles from Boston to Lynn ; how much farther is it
from Boston to Lynn than from Boston to Chelsea ?
9. From a board 16 feet long a carpenter cuts ofE
a piece 12 feet long; how many feet are left ?
10. A farmer gave 7 apples to John and 13 to
Helen ; how many more has Helen than John ?
11. If in an orchard containing 18 peach trees 5
trees are blighted, how many trees are healthy ?
12. A hen sits on 16 eggs ; 7 eggs spoil, the rest
hatch ; how many chickens are hatched ?
13. In a stable of 17 horses 6 have distemper;
how many are well ?
14. Of 18 loaves of bread a baker sells all but 7 ;
how many loaves does he sell ?
20 MENTAL ABITHMETIC.
XiSMon 20.
1. From 19 gallons of kerosene 9 gallons leaked
out ; how many gallons remained ?
2. A boy has 9 stamps; how many must he buy
to make the number 17 ?
3. George has 16 marbles, which is 9 more than
Frank has ; how many has Frank ?
4. A man walks 15 miles in a day ; if he walks 9
miles in the forenoon, how many miles does he walk
in the afternoon ?
5. I paid 14 dollars for a table and 5 dollars for a
chair ; how many more dollars did I pay for the table
than for the chair ?
6. A milkman had 18 cows ; how many did he
have after selling 9 of them ?
7. Of a flock of 17 turkeys how many were left
after a fox carried off 8 ?
8. Alice has 16 roses ; 7 are white, the rest red ;
how many are red ?
9. After I have walked 11 miles, how many shall
I have to walk to make 19 miles ?
10. If Fred had 8 more marbles he would have
15 ; how many marbles has he ?
11. One train has 9 cars and another has 16 ; how
many more cars has one than the other ?
12. Frank caught 17 trout, and Henry caught 8 ;
how many more did Frank catch than Henry ?
13. Lucy is 14 years old ; how old was she 6 years
ago?
14. There are 15 rolls on the table before supper,
and only 3 after supper ; how many rolls were eaten ?
SlEKTAIi ARITHMBTIO. 21
Ziesaon 21.
1. If I had 9 more children, I should hare 14 ;
how many children have I ?
2. A cook had 13 eggs, but used 6 for a pudding ;
how many eggs were left ?
3. My father and mother together gave me 18
cents ; my mother gave me 12 cents ; how many did
my father give me ?
4. I have in my pocket 16 cents ; one piece is a
ten-cent piece, and the others are one-cent pieces ; how
many one-cent pieces have I ?
5. Tom picked 12 quarts of cherries, Ida picked
7 ; how many more quarts did Tom pick than Ida ?
6. Charles had 15 cents, but spent 10 cents for
candy ; how many cents had he left ?
7. I paid 17 cents, postage on two bundles; the
postage on one was 6 cents ; how much was the post-
age on the other ?
8. In a class of 16 scholars, 5 are boys and the
rest are girls ; how many girls are there ?
9. Ked had 13 marbles, but gave away 5; how
many had he then ?
10. Ealph had 18 papers to deliver ; he has de-
livered 14 ; how many has he to deliver ?
11. If in two pods there were 12 peas, and in one
of the pods there were 6 peas, how many were there
in the other pod ?
12. Julia had 14 yards of ribbon, but has used 5
yards ; how many yards remain ?
13. A newsboy had 17 papers. After he had ^old
8 of them, how many had he left ?
22 MENTAL ARITHMETIC.
ZiMwon 22.
1. There were 14 eggs in the nest^ but 11 were
bad ; how many were good ?
2. From sap that I gathered I made 17 cakes of
maple sugar ; after giving away 9 cakes, how many
hadi?
3. Ned paid 19 dollars for a second-hand bicycle
and sold it for 8 dollars ; how many dollars did he
lose ?
4. By the direct road the distance to the city is
14 miles ; by the indirect it is 19 miles. How much
shorter is the direct road ?
5. It took me 15 minutes to skate up to the bridge
against the wind, but only 6 minutes to skate back ;
how many more minutes did it take me to skate up ?
6. Our Nine made 15 runs, the other Nine made 9
runs ; by how many runs did we beat ?
7. There were in the room 7 chairs and 16 persons ;
how many persons had to stand ?
8. In a certain year all but 6 of the 14 scholars
came from out of town ; how many came from out gf
town?
9. A boy had to go to a town 13 miles away. He
rode 8 miles, but had to walk the rest of the way.
How many miles did he walk ?
10. I spent 12 ^dollars for wood and coal. If I
paid 7 dollars for coal, how much did I pay for
wood?
11. Mary has 14 cents, and spends 5 cents for a
spool of silk. How many cents has she left for
ribbon ?
MENTAL ARITHMETIC. 23
LeBBon 23.
1. Of 13 cats and kittens, 5 were kittens ; how
many were cats ?
2. A farmer brought 16 dozen eggs to market, and
sold all but 4 dozen ; how many dozen did he sell ?
3. I have 18 lines of poetry to learn. After I
have learned 14 lines, how many lines shall I have to
learn ?
4. Three boys, Tom, Dick, and Harry, picked 17
quarts of berries. Tom picked 5 quarts, and Dick
picked 5 quarts. How many quarts did Harry pick ?
5. In a certain garden there are 18 trees, 6 of
which are pear, 7 peach, and the rest cherry. How
many cherry trees are there ?
6. A boy paid 8 cents for some oranges and sold
them for 12 cents ; how many cents did he make ?
7. In a flock of 16 sheep and lambs there are 7
lambs ; how many sheep are there ?
8. Three boys picked up 15 bushels of potatoes.
If one boy picked up 6 bushels, how many bushels
did the other two boys pick up ?
9. I have 19 minutes for play, but it takes me 7
minutes to make up my mind what to play. How
many minutes remain ?
10. From a flock of 17 lambs 8 were sold ; how
many lambs were left ?
11. A boy has 16 cents. If he spends 9 of them,
how many cents will he have left?
12. Henry, James, and Eeuben have together 18
cents. Henry has 4 cents and James has 5 ; how
many has Keuben ?
24 MENTAL ASITHMETIO.
LesBon 24.
1. How many are 7 — 6?
37 — 6? 47 — 6? 57 — 6?
87-6? 97-6?
2. How many are 8 — 6?
38-6? 48-6? 58 — 6?
88 — 6? 98 — 6?-
3. How many are 9 — 6?
39-6? 49-6? 59-6?
89 — 6? 99 — 6?
4. How many are 10 — 6?
40 — 6? 50 — 6? 60 — 6?
90-6? 100 — 6?
5. How many are 11 — 6 ?
41-6? 51 — 6? 61-6?
91 — 6? 101 — 6?
6. How many are 12—6?
42—6? 52 — 6? 62 — 6?
92-6? 102-6?
7. How many are 13 — 6 ?
43-6? 53-6? 63-6?
93-6? 103-6?
8. How many are 14 — 6?
44 — 6? 54-6? 64-6?
94-6? 104-6?
9. How many are 15 — 6 ?
45-6? 55-6? 65-6?
95-6? 105-6?
10. How many are 16 — 6?
46-6? 56-6? 66-6?
96-6? 106 — 6?
17-6?
27 — 6?
67-6?
77 — 6?
18-6?
28—6?
68-6?
78—6?
19-6?
29—6?
69-6?
79 — 6?
20-6?
30-6?
70 — 6?
80-6?
21-6?
31—6?
71-6?
81-6?
22-6?
32-6?
72—6?
82—6?
23 — 6?
33-6?
73-6?
83-6?
24-6?
34-6?
74 — 6?
84-6?
26-6?
36-6?
76-6?
86-6?
26 — 6?
36-6?
76 — 6?
86-6?
MENTAL ABITHMETIG. 25
Lesson 25.
1. How many are 8 — 7? 18 — 7? 28 — 7?
38-7? 48 — 7? 68-7? 68-7? 78-7?
88 — 7? 98-7?
2. How many are 9 — 7 ? 19 — 7 ? 29 — 7 ?
39 — 7? 49 — 7? 69 — 7? 69 — 7? 79 — 7?
89 — 7 ? 99 — 7 ?
3. How many are 10 — 7? 20 — 7? 30 — 7?
40 — 7? 60 — 7? 60 — 7? 70-7? 80-7?
90 -• 7 ? 100 — 7 ?
4. How many are 11 — 7? 21 — 7? 31 — 7?
41-7? 61—7? 61-7? 71-7? 81 — 7?
91-7? 101—7?
6. How many are 12 — 7? 22 — 7? 32 — 7?
42 — 7? 62 — 7? 62 — 7? 72 — 7? 82 — 7?
92-7? 102-7?
6. How many are 13 — 7? 23 — 7? 33 — 7?
43 — 7? 63-7? 63 — 7? 73 — 7? 83-7?
93 - 7 ? 103 - 7 ?
7. How many are 14 — 7? 24 — 7? 34 — 7?
44 — 7? 64 — 7? 64 — 7? 74 — 7? 84 — 7?
94 — 7 ? 104 — 7 ?
8. How many are 16 — 7? 26 — 7? 36 — 7?
45-7? 66-7? 66-7? 75-7? 86-7?
96 - 7 ? 105 - 7 ?
9. How many are 16 — 7? 26 — 7? 36 — 7?
46 — 7? 66 — 7? 66 — 7? 76 — 7? 86 — 7?
96—7? 106-7?
10. How many are 17 — 7 ? 27 — 7 ? 37 — 7 ?
47 — 7? 57-7? 67 — 7? 77 — 7? 87 — 7?
97 — 7? 107 — 7?
26 MENTAL ABITHMETIC.
LeBBon 26.
1. How many are 9 — 8? 19 — 8? 29 — 8?
39 — 8? 49 — 8? 69-8? 69 — 8? 79 — 8?
89-8? 99-8? 109-8?
2. How many are 10 — 8? 20 — 8? 30 — 8?
40-8? 50-8? 60-8? 70-8? 80-8?
90 — 8? 100—8?
a How many are 11 — 8? 21—8? 31—8?
41 — 8? 51—8? 61 — 8? 71 — 8? 81—8?
91 — 8 ? 101 - 8 ?
4. How many are 12 — 8? 22 — 8? 32 — 8?
42 — 8? 52 — 8? 62 — 8? 72-8? 82 — 8?
92-8? 102 — 8?
5. How many are 13 — 8? 23 — 8? 33 — 8?
43 — 8? 53 — 8? 63-8? 73 — 8? 83 — 8?
93 - 8 ? 103 - 8 ?
6. How many are 14 — 8? 24 — 8? 34 — 8?
44 — 8? 54 — 8? 64 — 8? 74 — 8? 84 — 8?
94 — 8 ? 104 — 8 ?
7. How many are 15-8? 25 — 8? 35 — 8?
45-8? 55 — 8? 65-8? 75 — 8? 85-8?
95 — 8? 105 — 8?
8. How many are 16 — 8? 26 — 8? 36 — 8?
46 — 8? 56-8? 66-8? 76 — 8? 86-8?
96 - 8 ? 106 - 8 ?
9. How many are 17 — 8? 27 — 8? 37 — 8?
47—8? 57-8? 67 — 8? 77 — 8? 87 — 8?
97 — 8? 107-8?
10. How many are 18 — 8? 28—8? 38 — 8?
48 — 8? 58-8? 68-8? 78 — 8? 88 — 8?
98 — 8? 108-8?
MENTAL ABITHMETIG. 27
Lesson 27.
1. How many are 10 — 9 ? 20 — 9 ? 30 — 9 ?
40 — 9? 60-9? 60 — 9? 70-9? 80 — 9?
90 — 9? 100 — 9?
2. How many are 11 — 9? 21—9? 31 — 9?
41-9? 61 — 9? 61 — 9? 71 — 9? 81 — 9?
91 - 9 ? 101 - 9 ?
3. How many are 12 — 9? 22 — 9? 32 — 9?
42 — 9? 62 — 9? 62 — 9? 72-9? 82 — 9?
92 - 9 ? 102 — 9 ?
4. How many are 13 — 9? 23 — 9? 33 — 9?
43 — 9? 63 — 9? 63 — 9? 73-9? 83 — 9?
93-9? 103 — 9?
5. How many ^are 14 — 9? 24 — 9? 34 — 9?
44-9? 64-9? 64-9? 74-9? 84-9?
94 — 9 ? 104 — 9 ?
6. How many are 15 — 9? 26 — 9? 36 — 9?
46 — 9? 65-9? 66 — 9? 75 — 9? 85 — 9?
95 — 9? 105-9?
7. How many are 16 — 9? 26 — 9? 36 — 9?
46 — 9? 66 — 9? 66 — 9? 76 — 9? 86-9?
96-9? 106-9?
8. How many are 17 — 9? 27 — 9? 37 — 9?
47 — 9? 67 — 9? 67 — 9? 77 — 9? 87 — 9?
97 — 9 ? 107 — 9 ?
9. How many are 18 — 9? 28 — 9? 38 — 9?
48-9? 68-9? 68-9? 78 — 9? 88-9?
98 - 9 ? 108 - 9 ?
10. How many are 19 — 9 ? 29 — 9 ? 39 — 9 ?
49-9? 69-9? 69-9? 79-9? 89-9?
99-9? 109-9?
28 MSKTAL ASITHMSTIO.
LeBBon 28.
How many are
23 35 33 37 32 31 28
-4 . —9 -5 —9 -7 —3 —9
24
27
21
22
46
26
35
-8
-8
-7
—6
— 7
-9
-6
36
41
43
42
51
56
61
-8
—4
— 6
— 7
— 6
— 7
-6
34
45
63
71
80
82
86
— 7
-8
— 6
— 7
-9
—3
— 7
76
48
70
98
74
64
94
— 7
-9
— 7
— 9
-7
-6
— 8
87
42
96
67
73
72
95
— 9
-9
— 7
— 9
-6
-9
— 6
62
86
73
85
91
93
64
-3
-6
— 7
-8
-9
-8
-8
56
56
76
86
80
87
93
— 7
— 7
— 9
-9
-3
-8
— 4
83
35
61 .
85
83
80
43
-8
— 6
— 7
— 7
-7
-8
— 9
51
73
92
62
72
61
82
-8
— 6
-9
— 8
— 7
-8
— 7
MENTAL ABITHMETIC. 29
29.
1. In a school of 23 pupils 9 are boys, and the
rest girls ; how many girls are there ?
2. In a grove of 27 trees 8 were blown down in a
storm ; how many remained standing ?
3. A farmer having 32 sheep sold 7 to a drover ;
how many remained ?
4. Joseph has 9 cents and Maggie has 27 cents ;
how many innst be given to Joseph that he may have
as many as Maggie ?
5. The snm of two numbers is 35 ; one number is
8 ; what is the other number ?
6. I have 9 dollars towards a bicycle that costs 42
dollars; how many more dollars do I need to buy
the bicycle ?
7. A man receives 30 dollars for a week's work,
and a boy receives 9 dollars ; how many dollars does
the man receive more than the boy ?
8. A florist has 37 roses, 9 of which are white,
and the rest red ; how many are red ?
9. I had 21 tons of hay, but sold 8 tons ; how many
tons remained ?
10. A garden has 56 hills of com and squashes ;
there are 8 hills of squashes ; how many hills of corn
are there ?
11. I give a man 25 dollars in payment for a suit
of clothes, and he gives me back 9 dollars in change ;
what is the price of the suit ?
12. A freight train of 27 cars starts from Boston
for New York ; 9 cars are left on the way ; how many
cars go through ?
30 MENTAL ABITHMETIC.
LoBson 30.
1. A drover starts with 53 sheep, but 8 stray away ;
how many are left ?
2. A city has 73 miles of streets, all but 9 miles
of which are paved ; how many miles are paved ?
3. A father is 32 years old and his son 5 ; how
much older is the father than his son ?
4. Two boys bought a ball for 75 cents ; one paid
8 cents ; how many cents did the other pky ?
5. Of a flock of 93 sparrows, all but 7 were killed ;
how many were killed ?
6. By selling a watch for 81 dollars I make a profit
of 9 dollars ; what did the watch cost me ?
7. I have gained 7 pounds in two months, and now
weigh 76 pounds ; how many pounds did I weigh two
months ago ?
8. John is 8 inches shorter than his brother Henry ;
Henry is 63 inches tall ; how tall is John ?
9. This month has 31 days, but 7 days are gone ;
how many days remain ?
10. Of the 82 guests present only 8 made speeches ;
how many did not make speeches ?
11. In a class of 55 pupils, 6 failed to graduate j
how many graduated ?
12. A book had 98 pages, but 9 are torn out ; how
many pages remain ?
13. There were 87 passengers when the train
started, but only 8 when it reached the last station ;
how many stopped on the way ?
14. I had 34 marbles, but lost all but 7 ; how
many did I lose ?
MENTAL ARITHMETIC. 81
Lesson 31.
1. I gave the ticket agent a 20-dollar bill for a
ticket that costs 7 dollars. How many dollars ought
I to receive in exchange ?
2. A man started on a journey with 85 dollars.
After he had spent 9 dollars how many dollars had
he?
3. John has earned 8 dollars towards paying for a
65-dollar bicycle. How many more dollars- must he
earn ?
4. My father put 83 pounds of ice into his refrig-
erator in the morning, but only 5 pounds remained
the next morning. How many pounds had melted ?
5. In a party of 41 children 6 belonged to one
family. How many belonged to the other families ?
6. There are 62 buildings in a certain village, 6
of which are stores. How many are not stores ?
7. If I sleep 8 of the 24 hours a day, how many
hours remain for other purposes ?
8. If the sum of two numbers is 67, and one num-
ber is 9, what is the other number ?
9. What must be added to 8 to make 87 ?
10. The distance from Athol to North Adams is
61 miles, and from Hoosac Tunnel to Korth Adams
8 miles. How far is it from Athol to Hoosac
Tunnel ? ^
11. I travelled 92 miles. The first 7 miles I rode
in a carriage, and the remainder in the cars. How
far did I ride in the cars ?
12. I give the hotel clerk 40 dollars, and he gives
me back 6. How much is my bill ?
32
HBNTAI. ABITHUBTIO.
IiOBaoii 32.
BfULTIPUCATION TABTiH
2
3
4
6
times
times
times
times
1 are
2
1 are 3
1 are 4
1 are 5
2 are
4
2 are 6
2 are 8
2 are 10
3 are
6
3 are 9
3 are 12
3 are 15
4 are
8
4 are 12
4 are 16
4 are 20
5 are
10
5 are 15
5 are 20
5 are 25
6 are
12
6 are 18
6 are 24
6 are 30
7 are
14
7 are 21
7 are 28 •
7 are 35
8 are
16
8 are 24
8 are 32
8 are 40
9 are
18
9 are 27
9 are 36
9 are 45
10 are
20
10 are 30
10 are 40
10 are 50
11 are
22
11 are 33
11 are 44
11 are 55
12 are
24
12 are 36
12 are 48
12 are 60
6
7
8
9
times
times
times
times
1 are
6
1 are 7
1 are 8
1 are 9
2 are
12
2 are 14
2 are 16
2 are 18
3 are
18
3 are 21
3 are 24
3 are 27
4 are
24
4 are 28
4 are 32
4 are 36
5 are
30
5 are 35
5 are 40
5 are 45
6 are
36
6 are 42
6 are 48
6 are 54
7 are
42
7 are 49
7 are 56
7 are 63
8 are
48
8 are 56
8 are 64
8 are 72
9 are
64
9 are 63
9 are 72
9 are 81
10 are
60
10 are 70
10 are 80
10 are 90
11 are
66
11 are 77
11 are 88
11 are 99
12 are
72
12 are 84
12 are 96
12 are 108
MENTAL ABITHMETIC. 38
Lesson 33.
1. 9 times 12 are 108. How many are 12 times 9 ?
8 times 11 are 88. How many are 11 times 8 ?
2. 11 times 12 are 132. How many are 12 times
11 ? 12 times 12 are 144. How many are 12 dozen ?
10 times 11 are 110. How many are 11 times 11 ?
3. George has 2 rabbits, and Henry has 6 times
as many. How many has Henry ?
4. What must be paid for 7 yards of silk velvet
at 2 dollars a yard ?
5. A boy picks 3 quarts of blackberries every
day. How many quarts will he pick in 6 days ?
6. What will 8 pencils cost at 3 cents each ?
7. What must I pay for 9 two^ent postage stamps ?
8. A plumber earns 3 dollars a day. How much
does he earn in 6 days ?
9. There are 4 quarts in one gallon. How many
quarts are there in 7 gallons ?
10. If there are 4 panes of glass in one window,
how many panes are there in 9 windows ?
11. What will 6 cords of wood cost at 4 dollars a
cord?
12. In 8 five-dollar bills how many dollars are
there ?
13. If a farmer cuts 5 tons of hay on 1 acre, how
many tons will he cut on 6 acres ?
14. How much will 9 quarts of milk cost at 5 cents
a quart?
16. A fly has 6 legs. How many legs have 6 flies ?
16. How many pounds of butter will there be in 8
six-pound packages ?
34 MENTAL ABITHMETIC.
Xiesaon 34.
1. A horse goes 6 miles in 1 hour. How far will
he go in 7 hours ?
2. How much must be paid for 4 tons of coal at 6
dollars a ton ?
3. If a yard of muslin costs 6 cents, what will 12
yards cost ?
4. If 6 persons can sit on 1 bench, how many can
sit on 8 benches ?
5. A- restaurant uses 6 dozen eggs a day. How
many dozen will it use in 7 days ?
6. In a week there are 7 days. How many days
^ are there in 7 weeks ? In 9 weeks ?
7. How many pounds of grapes are there in 8 boxes
weighing 7 pounds each ?
8. At 6 cents each what will 9 oranges cost ?
9. . If a man pays 7 dollars rent each month, how
much will he pay in a year, or 12 months ?
10. A horse travels 7 miles an hour, and a railroad
train travels five times as fast. How far does the train
travel in an hour ?
11. If mackerel are worth 7 cents each, how much
must be paid, for 6 of them ?
12. If a family uses 8 cents' worth of oil in a day,
how much will it use in 3 days ?
13. A carpenter saws a board into 4 lengths of 8
feet each. How long was the board ?
14. If a clerk copies 8 pages a day, how many
pages will he copy in 5 days ? In 8 days ?
15. If a barge can carry 12 persons, how many
per80U9 can 9 barges carry ?
MEKTAL ABITHMETIC. 35
LesBon 35.
1. A farmer sells 12 dozen of green oom at 8 cents
a dozen. What does he receive ?
2. Charles's hens lay 8 eggs a day. How many
will they lay in 6 days ?
3. If 1 can of milk contains 8 quarts, how many
quarts will 8 cans contain ?
4. Each of 7 children has 8 dollars. How many
dollars have all the children ?
5. What shall I have to pay for 12 bottles of ink
at 8 cents a bottle ?
6. If 1 turkey weighs 8 pounds, how much will 11
turkeys of the same size weigh ?
7. At 9 cents a bunch, how much will 2 bunches
of celery cost ?
8. How many hills of corn are there in 2 rows of
9 hills each ?
9. What is the distance round a three-sided field
each of whose sides is 9 feet ?
10. A steamer sails 9 miles an hour. How far will
it sail in 6 hours, at the same rate ?
11. How much will 8 pounds of fish cost at 9 cents
a pound ?
12. Each length of a rail fence is 9 feet. How
many feet are there in 9 lengths ?
13. If a compositor sets 9 pages of type in 1 day,
how many pages will he set in 5 days ?
14. A laborer earns 9 dollars a week. How much
will he earn in 7 weeks ? In 11 weeks ?
15. Find the cost of 2 melons at 10 cents each.
36 MENTAL ABITHMETIO.
IiMSOn 3&
1. What must I pay for 3 pairs of blankets at 10
dollars a pair ?
2. A dime is 10 cents. How many cents are there
in 6 dimes ?
3. How many cords are there in 4 piles of wood^
each pile containing 10 cords ?
4. At 10 dollars a barrel what will a grocer receive
for 9 barrels of flour ?
5. What will 12 yards of cloth cost at 10 cents a
yard?
6. If a bushel of charcoal is worth 11 cents^ what
are 2 bushels worth ?
7. A farmer sets out 3 rows of trees with 11 trees
in each row. How many trees does he set out ?
8. If cranberries are selling at 11 cents a quart,
what must I pay for 3 quarts ? For 5 quarts ?
9. A boy rides 11 miles an hour on his bicycle.
How far will he ride in 11 hours, at the same rate ?
10. If a man and his wife pay 11 dollars a week
for board, how much will they pay in 6 weeks ?
11. A droyer sells 9 head of cattle at a profit of 11
dollars each. What is his profit on all the cattle ?
12. Eight boys each catch 11 fish. How many do
all catch ?
13. What will a boy receive for 2 quarts of berries
at 12 cents a quart?
14. There are 12 eggs in 1 dozen. How many are
there in 3 dozen ? In 6 dozen ? •
15. There are 12 inches in a foot. How many
inches are there in 4 feet ? In 6 feet ?
MENTAL ABITHMETIO. 37
Lesson 37.
1* At 12 cents an hour, how much will a boy earn
in 8 hours ?
2. If a cow produces 12 pounds of butter a week,
how many pounds will she produce in 10 weeks ?
3. If steel rails are 12 feet long, how far will 12
such rails reach if placed end to end ?
. 4. There are 12 books on each of 9 shelves of a
book-case. How many books are there in all ?
5. How many acres are there in 4 fields of 12 acres
each?
6. If a man works 12 hours a day for 6 days, how
many hours does he work in all ?
7. If I get 12 pounds of honey from 1 hive of bees,
how many pounds shall I get from 7 hives, at the
same rate ?
8. How much milk will 9 twelve-quart cans hold ?
9. Three feet make a yard. How many feet are
there in 9 yards ?
10. At 9 dollars a month, how much will a girl
earn in 3 months ? In 4 months ? In 6 months ?
11. A man walks 4 miles an hour. How far will
he walk in 7 hours ?
12. A horse travels 7 miles an hour. How far
will he travel in 4 hours ?
13. What will 12 sheep c<^t at 5 dollars each ?
14. If a grocer buys eggs at 12 cents a dozen and
sells them at 15 cents a dozen, how much will he gain
on 6 dozen ?
15. If a boy picks 12 quarts of blackberries a day,
how many quarts will he pick in 6 days ?
88 BfENTAL ARITHMETIC.
Lesson 38.
1. How many hours will it take one man to do
the work which 8 men do in 12 hours ?
2. A printer receives 25 dollars a month, but spends
13 dollars. How much will he save in a year, or 12
months ? *
3. If a barrel of flour lasts 12 persons 1 month,
how long will it last 1 person ?
4. If 1 horse eats 2 bushels of g^ain a week, how
many bushels will 8 horses eat ?
5. If 1 person eats 2 ears of com, how many ears
will be required for 12 persons ?
6. If 3 pipes of equal size fill a tank in seven
hours, how long will it take 1 pipe to fill it ?
7. At 7 dollars a ton, what must I pay for 9 tons
of coal ?
8. At 8 cents a quart, what will 8 quarts of blue-
berries cost ?
9. At 6 cents a quart, what will 9 quarts of milk
cost?
10. At 7 cents a pound, what will 8 pounds of
rice cost ?
11.- If it takes a boy 5 minutes to walk a certain
distance, how many minutes will it take him to walk
6 times as far ?
12. A spider has 8 legs. How many legs have 6
spiders ?
13. What must I pay for 9 cords of wood at 5 dol-
lars a cord ?
14. James has 7 cents. John has 7 times as many
cents. How many cents has John ?
MENTAL ARITHMETIC. 39
XiesBon 39.
1. How many seats are in 7 rows of 9 seats each ?
2. At 7 cents a quart, what must I pay for 8
quarts of beans ?
3. If a freight train averages 8 miles an hour, how
many miles will it run in 8 hours ?
4. At 8 dollars apiece, what will 12 calves cost ?
5. What must I pay for 12 two-cent postage
stamps ?
6. If I pay 5 dollars for a vest, twice as mifch for
trousers, and twice as much for coat as for trousers,
how much do I pay for the suit ?
7. If a family uses 9 pounds of sugar a week, how
many pounds will it use in 9 weeks ?
8. If it takes 6 eggs for a cake, how many eggs
will be required for 11 cakes ?
9. If a man sleeps 8 hours every night, how many
hours will he sleep in 7 nights, or one week ?
10. A farmer sold 8 pigs at 3 dollars each. How
much did he receive ?
11. How many trees are there in an orchard of 12
rows, 12 trees in a row ?
12. At an average of 12 examples on a page, how
many examples will there be on 9 pages ?
13. What will 12 quarts of beans cost at 7 cents
a quart ?
14. If a peck of oats weighs 8 pounds, how much
will 4 pecks, or a bushel, weigh ?
15. At 11 dollars a ton, what will 12 tons of can-
nel coal cost?
16. At 11 cents apiece, what will 11 cakes cost ?
40 HEKTAL ARITHMETia
Lesson 40.
DIVISION TABLE.
2-f-2 = l 3-h3 = l 4^4 = 1 5-^-6 = 1
4-5-2 = 2 6-r-3 = 2 8-7-4 = 2 10-5-5 = 2
6-^2 = 3 9-i-3 = 3 12-f-4=3 15^5 = 3
8-^^2 = 4 124-3 = 4 16-h4 = 4 20-5-5 = 4
10-T-2 = 6 16-5-3 = 6 20-5-4 = 6 25^5 = 6
12-^2 = 6 18-5-3 = 6 24-5-4 = 6 30^6 = 6
14-5-2 = 7 21-5-3 = 7 28-5-4 = 7 36-5-6 = 7
16-f-2 = 8 24-5-3=8 32-^-4 = 8 40-5-5 = 8
18-5-2 = 9 27-^3 = 9 36-^4 = 9 46-5-6 = 9
6-5-6 = 1 7-5-7 = 1 8-5-8 = 1 9-f-9 = l
12-^6 = 2 144-7 = 2 16-5-8 = 2 18-5-9 = 2
18^6 = 3 21-5-7 = 3 24-^8 = 3 27-5-9 = 3
244-6 = 4 28-f.7 = 4 324-8 = 4 364-9 = 4
304-6 = 5 354-7 = 6 40-^8 = 5 46-5-9 = 6
36-5-6 = 6 42-^7 = 6 484-8 = 6 64-5-9 = 6
424-6 = 7 494-7 = 7 66-^8 = 7 634-9 = 7
48-^-6 = 8 664-7 = 8 644-8 = 8 72-^9 = 8
64-5-6 = 9 63-f-7 = 9 72-f.8 = 9 81-^9=9
MEKTAIi ARITHMETIC. 41
IieBBon 41.
1. At 2 cents each, how many pears can I buy for
4 cents ?
2. If a man walks 8 miles in 2 hours, how far will
he walk in one hour ?
3. If I pay 10 dollars for 2 weeks' board, what is
the rate a week ?
4. If a boy picks 12 quarts of berries in 2 days,
how many quarts does he pick in one day ?
5. Two dozen screws cost 14 cents. What is the
price of one dozen ?
6. When bananas sell for 3 cents each, how many
can be bought for 15 cents ?
7. At 6 dollars a cord, how many cords of wood
can be bought for 18 dollars ?
8. If a family uses 24 pounds of butter in 3
weeks, how many pounds will it use in one week ?
9. With 30 dollars, how many cords of wood can I
buy at 6 dollars a cord ?
10. A grocer sells 48 gallons of molasses in 6
days. What is his average sale each day ?
U. How many four-cent stamps can I buy for 40
cents ?
12. Two yards of ribbon cost 24 cents. What is
the price of one yard ?
13. Mary's grandmother is 72 years old, 9 times
as old as Mary. How old is Mary ?
14. At 10 cents a pound, how much fish can be
bought for 30 cents ?
15. A horse eats 90 quarts of oats in 9 days. How
many quarts does he eat in one day ?
42 MENTAL ARITHMETIC.
LeMon 42.
1. At the rate of 12 miles an hour, how many
hours will a freight train require to run 36 miles ?
2. How many weeks will it take a man to earn 96
dollars if he earns 12 dollars each week ?
3. How many men will be required to do in 3 days
a piece of work which one man can do in 36 days ?
4. When eggs are selling at 12 cents a dozen, how
many dozen can be bought for 60 cents ?
5. Divide 21 oranges equally among 3 boys. How
many oranges will each boy receive ?
6. How many three-cent stamps can I buy for 27
cents ?
7. There are 24 feet in eight yards. How many
feet are there in one yard ?
8. I pay 36 cents for 4 quarts of berries. What
is the price of one quart ?
9. Frank pays 28 cents for 4 cakes of maple sugar.
What is the price of one cake ?
10. If it takes 32 days for one man to build a
wall, how many days will it take 4 men ?
11. At 6 cents a quart, how many quarts of milk
can I buy for 42 cents ?
12. In 5 bushels there are 20 pecks. How many
pecks are there in one bushel ?
13. At 7 dolle.rs a ton, how many tons of coal can
be bought for 56 dollars ?
14. If 5 gallons of oil cost 60 cents, what is the
price of one gallon ?
15. When melons are 12 cents each, how many
can be bought for 72 cents ?
MENTAL ABITHMETIG. 43
IiesBon 43.
1. One bottle of ink costs 8 cents. How many
bottles can be bought for 64 cents ?
2. A boy works 9 weeks and receives 36 dollars.
At the same rate, what would he receive for 1 week ?
for 2 weeks ? for 3 weeks ?
3. At 5 cents a pound, how many pounds of sugar
can be bought for 55 cents ?
4. In 12 hours 108 horses cross a certain bridge.
What is the average number an hour ?
5. There are 132 examples on 11 pages. What is
the average number on one page ?
6. If a blacksmith can shoe 66 horses in 6 days,
how many horses can he shoe in 12 days ?
7. I pay 144 cents for an advertisement of 12
lines. What is the rate jjer line ?
8. A farmer sold 6 barrels of apples for 18 dollars.
At the same price, what would he receive for 24
barrels ?
9. During the term a teacher orders 48 books for
a class of 12 pupils. What is the average number of
books required for one pupil ?
10. My hens lay 54 eggs a week, an average of 6
for each hen. How many hens have I ?
11. A secretary wrote 72 letters in 6 days. What
was the average number that he wrote in one day ?
12. My horse travelled 42 miles in 7 hours. What
was his rate per hour ?
13. After subtracting 16 from 100, there ^ill re-
main a number 7 times tbe stge of my oldest son,
Jiow oW is ie ?
44 MENTAL ABITHMETIO.
Lesson M.
1. For 6 dozen of eggs at 12 cents a dozen, a
woman received 9 yards of cloth. What was the
price of the cloth per yard ?
2. A farmer exchanged 10 cords of wood at 6 dol-
lars a cord for 12 barrels of flour. What was the
price of the flour per barrel ?
3. How many pounds of sugar at 6 cents a pound
should be received in exchange for 9 quarts of ber-
ries at 8 cents a quart ?
4. I paid 70 dollars for 10 weeks' board. What
was the rate per week ? per day ?
5. If a quantity of provisions will last 1 man 72
days, how long will it last 12 men ?
6. If you add 6 to 78, how many times 12 will
you have ?
7. How many days will 11 men need to do a piece
of work which 1 man can do in 88 days ?
8. How many tons of coal at 8 dollars a ton must
be given for 12 cords of wood at 6 dollars a cord ?
9. When 4 tons of coal are worth 24 dollars, 10
tons are exchanged for 12,000 shingles. What is the
price of the shingles per thousand ?
10. If 4 barrels of sugar are worth 48 dollars, how
many cords of wood at 6 doUats a cord must be given
for 2 barrels of sugar ?
11. On his way to market with 14 lambs, a drover
lost 5. At what rate must he sell the remainder to
receive 45 dollars ?
12. Find the cost of 7 yards of cloth when 5 yards
cost 60 cents.
MENTAL ABITHMETIG. 45
LoBBon 45.
1. I have 25 cents with which to buy two-cent
stamps. How many stamps can I buy, and how
much money shall I have left ?
2. A boy with 12 cents bought 2 dozen rubber
rings at 5 cents a dozen. How many rings did he
buy, and what sum had he left ?
3. At 7 dollars a ton, how many tons of coal can
I buy for 63 dollars ?
4. How many yards of muslin at 12 cents a yard
can a girl buy for 108 cents ?
5. How many peaches at 10 cents a dozen can I
buy for 25 cents ?
6. What is the smallest number that must be
taken from 25 to leave a number exactly divisible
by 3?
7. A boy exchanged 9 quarts of chestnuts at 10
cents a quart for twelve quires of paper, and received
6 cents in money. What was the price of the paper
per quire ?
8. How many yards of velvet at 5 dollars a yard
can a milliner buy for 59 dollars, and how much
money will she have left?
9. How many pounds of sugar at 6 cents a pound
can I buy for 75 cents, and how much money shall I
have left ?
10. If I give a conductor a fifty-cent piece for 8
six-cent fares, how much ought he to give me back ?
11. A lady received 4 dollars from 4 ten-dollar
bills after paying for coal at 6 dollars a ton. How
many tons did she buy ?
46 MENTAL ARITHMETIO.
V
Leaaon 46.
Name the
quotient and the remainder of
3-^2
6-J-3
6^4
12-5-6
6-1-2
8-4-3
9-5-4
18-4-6
7-1-2
11-1-3
16^4
23-5-6
9-S-2
13^-3
19^-4
29-5-6
11^2
19-4-3
27-5-4
31-4-6
15-4-2
23-5-3
29-4-4
43-4-5
17-4-2
29-4-3
37 : 4
49-5-6
19-S-2
31 : 3
39-5-4
67^6
21-5-2
35-5-3
43-5-4
69-4-6
23 -s- 2
37-5-3
49-5-4
62-5-6
9-4-6
13-5-7
16-5-8
17-5-9
13-5-6
17-4-7
21-4-8
23-4-9
17^6
26^7
33-5-8
39 : 9
27-4-6
39-5-7
45-5-8
47-5-9
31 : 6
48-5-7
51-5-8
66-5-9
43-4-6
61-5-7
59^-8
68-5-9
66^6
59^7
63-5-8
71-5-9
69-4-6
66-4-7
77-5-8
78-5-9
65^6
78-5-7
89-4-8
86-5-9
73-*-6
83-5-7
96-5-8
89 -i- 9
MxarcAx AjaTBXETOL a
1. I liaY6 55 IsiittoiiB to ftrxange in biz 6q[izBl tows.
How many rnuEt I put in a row, and how many shall
I have left ?
2. A f orenian reoeives 7 doIlarB foar 2 dq^' woik.
What is his rate a day ?
a If a freight trin rux« 24 maeB in 2 honxB,
how far will it run in 4 hours ?
4. At 8 cents a quart, how many quarts of beans
can be bought for 60 o^xts, and how much of the
money will be left ?
5. If 9 sheep cost 54 dollars, what is tbe cost of
12 sheep ?
6. I pay 36 dollars for 4 tons af cannel ooaL
What win be the cost of 12 tons ?
7. If I pay 32 cents for a can of 6 quarts of milk,
what will be the cost of 7 quarts ?
8. How long will 64 pounds of sugar last a family
that uses 12 pounds a week ?
9. If yon sleep 24 hours in 3 nights, how many
hours at the same average will you sleep in 12 nights ?
10. A man receives 45 dollars for 5 loads of
bricks. What will be the cost of 7 loads ?
U. If a man can build 84 yards of fence in 6
days, how many yards can he build in 3 days ?
12. A dealer sol^ 4 plows for 32 dollars. What
will be the cost of 7 plows ?
13. Kine tons of coal cost 63 dollars. What is
the cost of 7 tons ?
14. There are 8 quarts in one peck, and 4 pedkB
in one bnshel. How many bushels in 64 quarts?
48 HBNTAL ABITHMSTIC.
ZiOMoa 48.
1. If 4 pounds of sugar cost 28 cents, what will 11
pounds cost ?
2. A boy has 10 quarts of berries at 8 cent^ a
quart to exchange for oil at 10 cents a gallon. How
much oil will he receive ?
3. At the rate of 10 miles in 3 hoursi how far will
a man row in 9 hours ?
4. If a horse can travel 36 miles in 6 hours^ how
far will he travel in 12 hours ?
5. If a man walks 12 miles in 3 hours, what is his
rate an hour ? How far will he walk in 7 hours ?
6. A boy has 35 cents with which to buy 3 pen-
cils at 5 cents each and 2 blank books at 8 cents each.
How much money will he have left ?
7. Sixteen apples are divided among 4 boys. How
many apples will 3 boys get?
8. Thirty-six yards of cloth are needed for 12
coats. How many yards are needed for 24 coats ?
9. If 2 pencils cost 8 cents, how many can be
bought for 25 cents ? How much money will be left ?
10. A field of 100 acres is divided into 25 equal
lots. How many acres does each lot contain ?
11. Four persons wish to share equally a bill of
36 dollars. How much must each pay ?
. 12. If 5 tons of coal cost 35 dollars, what is the
cost of 9 tons ?
13. The pay-roll for 12 men amounts to 36 dollars
a day. What does each man receive ?
14. At the rate of 54 cents for 6 pencilSi what will
12 pencils cost ?
MENTAL ABITHMETIO. 49
LesBon 49.
1. At 7 dollars a ton, how many tons of coal can I
buy for 50 dollars, and how much money will be left ?
2. From 150 dollars I have 6 dollars left after pay-
ing 12 men. What is the average sum paid each man ?
3. If 4 bushels of potatoes are worth 1 bushel of
wheat, and 6 bushels of wheat are worth 1 barrel of
flour, how many bushels of potatoes must be given
for 2 barrels of flour ?
4. If a certain field is divided into 6 equal parts,
each part will contain 6 acres. How many acres will
there be in each part if the field is divided into 4 equal
parts?
5. If John's money is divided into 8 equal parts
there will be 4 cents in each part. How many cents
will there be in each part if it is divided into 4 equal
parts ? into 2 equal parts ? into 16 equal parts ?
6. If 8 men can build a fence in one day, how
many men must be employed to build it in 2 days ?
7. If 8 men can build a fence in 2 days, how many
men must be employed to build it in one day ?
8. If it takes 8 men 4 days to build a fence, how
many days will it take 4 men to build it ? 16 men ?
9. If 6 men can build a barn in 40 days, in how
many days can 8 men build it ?
10. If 3 men can mow a certain field in 12 days,
how many days will it take 4 men to mow it ?
11. If 8 men can build a certain wall in 9 days,
how many men will build it in 3 days ?
12. If the value of 8 sheep is 72 dollars; what is
the value of 6 of the sheep ?
CHAPTER 11.
COMPOUND QUANTITIBS.
Lesson 1.
UNITilD STATES MONET.
Table.
10 mills = one cent.
10 cents = one dime.
10 dimes = one dollar.
100 cents = one dollar.
The coins in common use are the cent, the nickel (five cents),
the dime (ten cents), the quarter (twenty-five cents), the haJf
(fifty cents), the dollar (one hundred cents).
The dollar sign ($) is placed before the figures.
. The dot, or decimal point, is placed between the dollars and
the cents ; thus, $6.50 is read *^five dollars and fifty cents.*'
1. How many cents are there in a quarter of a dol-
lar ? How many are there in a half-dollar ?
2. How many two-cent postage stamps can I buy
for 25 cents ? Shall I have any money left ?
3. One dozen cedar pencils cost 10 cents. How
many dozen can I buy for one dollar ?
4. If I give a five-dollar bill in payment for boots
that cost $4.50, how much change shall I receive?
5. What will 5 quires of paper cost at 25 cents a
quire ?
6. A boy buys a gallon of oil for 10 cents, a pound
of soda for 10 cents, and a yeast cake for 2 cents. If
he gives a quarter in payment, how much change
will he receive ?
MENTAL ABITHMETIC. 51
Lesson 2.
1. Wliat will 9 barrels of flour cost at $5.10 a
barrel ?
2. At the rate of $3.15 each; how much will 5
hats cost ?
3. What will 4 pounds of beefsteak cost at 25 cents
a pound ?
4. A boy has earned $15.50 towards the pur-
chase of a bicycle that costs $25. How much more
must he earn ?
5. A man buys a coat for $12.50 and a vest for
$5.50. He gives in payment two ten-dollar bills.
How much change ought he to receive ?
6. A man gives four ten-dollar bills in payment
for the use of a hall six nights at $6 a night. How
much change must he receive ?
7. What will 5 pounds of coffee cost at 30 cents
a pound ?
8. What will 4 tons of coal cost at $7.25 a ton ?
9. At $3.50 a cord, how many cords of pine wood
can be bought for $7 ?
10. At the rate of 2 cents a mile, what will a
mileage book of 1000 miles cost ?
11. What will be the amount of my hotel bill for
four days at the rate of $2.50 a day ?
12. Five times 2Q cents are how many times
25 cents ?
13. A carpenter receives 25 cents an hour. How
much will he receive for 6 hours' work ?
14. A boy is paid 15 cents an hour for raking
leaves. How much will he earn in 7 hours ?
62 MXNTAL ABITHHBTIO.
LeMon 3.
L John goes to town with $1. He pays 50
cents for sugar, 10 cents for soda, 15 cents for cod-
fish, and the remainder for a book. What does he
pay for the book ?
2. I offer a five-dollar bill in payment for books.
One book costs $1.25, another 75 cents, another 50
cents. How much change ought I to receive ?
3* How much must I pay for two railroad tickets
at $1.20 each and three half-tickets at 60 cents each ?
4. I buy a mileage book for $20, a hat for $4,
a pair of boots for $3.50, and a pair of overshoes for
$3.50. How much do I spend ?
5. At the rate of 2 cents a mile for each person,
how much will it cost 4 persons to ride 51 miles ?
6. I buy a turkey weighing 10 pounds, give in
payment a two-dollar bill and receive in change
20 cents. What is the price of the turkey a pound ?
7* My friend pays $20 for a mileage book. After
he uses it on a road that charges 2 cents a mile, he
sells the book to me for $18.70. How many miles
did be ride ?
8. I give a ten-dollar bill in payment for three
books of equal value and receive $2.50 in change.
What is the price of each book ?
9. I buy three books. The second costs twice
as much as the first, and the third twice as much as
the second. The third costs $10. What is the cost
of each of the others, and of all together ?
10. If a man receives $1.50 for 6 houro work,
what is the rate per hour ?
MBNTAL ABITHMXTIO* 63
^etMon 4.
1. A boy has $S in ten-cent pieces. How many
pieces has he ?
2. How many five-cent postage stamps can be
bought for $1.50 ?
3. At 25 cents a dozen, how many dozen oranges
can be bought for $1.25 ?
4. At the rate of three apples for 2 cents how
many apples can be bought for $1 ?
5. I spend $1 for postage stamps. tThe number
of one-cent stamps that I buy is equal to the number
of cents that I pay for the two-cent stamps. How
many stamps of each kind do I buy ?
6. How much postage must I pay on 25 letters at
2 cents each, 20 newspapers at 1 cent each, fifteen
circulars at 1 cent each, and a book at 20 cents ?
7. I have 5 five-dollar bills. How much money
shall I have left after paying my tailor $18.50, my
shoemaker $5.50, and my barber 25 cents ? '
8. If a workman is paid at the rate of $2.50 a
day, how many days must he work to earn enough
to pay his doctor's bill of $25 ?
9. What will 3000 cubic feet of gas cost at $2.30
a thousand ?
10. One person gives $5 towards a present that
costs $10.50, another gives $3, and another gives the
remainder. How much does the third person give ?
U. A boy receives $1 from his mother, twice as
much from his father, and twice as much from his
sister as from his father. How much does he re-
ceive ?
I
54 liEKTAL ABITHMETIO.
Lmboii 5.
LIQX7ID BffXSASITRE.
Liquid Measure is used in measuring liquids, as water,
milk, etc.
Table.
4 gills (gi.) = 1 pint (pt.).
2 pints = 1 quart (qt.).
4 quarts = 1 gallon (gal.).
Hence, 1 gal. = 4 qts. = 8 pts. == 32 gi.
1. From a cask that held 24 gallons and 2 quarts,
2 gallons and 2 quarts were drawn off. How much
was left in the cask ?
2. I paid a farmer 68 cents for making my cider.
He charged 2 cents a gallon. How many gallons did
I have ?
3. A milkman sells a large can (two gallons) of
milk for 32 cents. What is the rate a quart ?
4. Is it cheaper to buy a large can (two gallons)
of milk at 35 cents, or 8 quarts at 5 cents a quart ?
5. If oil is 12 cents a gallon, what will a quart
cost?
6. Pure vanilla sells for f 1.60 a pint. What
would a quart cost at the same rate ? A gallon ?
7. Thirty gallons of syrup cost f 27. What was
the rate a gallon ?
8. If alcohol sells for 60 cents a quart, what must
I pay for a pint ? For a gallon ?
9. If 1 pint of cologne costs $1, how much will
a gallon cost ? A gill ?
10. At the rate of 90 cents a quart, how. much
must I pay for a gallon of olive oil ?
MENTAL ABITHMETIC. 55
LeBBon 6.
1. There are 63 gallons in a hogshead. If a cistern
holds 100 hogsheads, how many gallons does it hold ?
2. What must I pay for 31 gallons of milk at 5
cents a quart ?
3. A man pays $4.80 for a cask of vinegar. If
the cask holds 24 gallons what is the rate a gallop ?
4. If a dealer pays $2 for a 10-gallon cask of
vinegar, what is the rate a quart ?
5. How many bottles, each holding 1 gill, can be
filled with a quart of ink ?
6. My lamp holds 1 pint. How many times can
I fill it with a gallon of oil ?
7. If a pint of oil lasts me two nights, how many
quarts shall I burn in 16 nights ?
8. One quart of raspberries when cooked will fill a
pint can. How many quarts of raspberries when
cooked will be required to fill 4 one-quart cans ?
9. From my two-quart pitcher full of water 1 can
fill eight glasses. How much does each glass hold ?
10. How large must eight bottles of equal size be
to contain exactly two gallons of syrup ?
. 11. The tub which I use for a rain gauge is 4
inches deep, and holds 10 quarts. When it is filled
to the depth of 1 inch, how many pints of water are
there in it ?
12. If oil is 16 cents a gallon, how much will 2
gallons and 2 quarts cost?
13. My milk bill for 30 days is $6. If I pay 4
cents a quart, how many quarts of milk do I buy per
day?
06 MENTAL AKITHMSnC.
ZieMKm7.
Dry Measure is oted in measuring dry articles, aft grain,
seeds, fruit, vegetables.
Tablb.
2 pints (pt.) = 1 quart (qt.).
8 quarts = 1 peck (pk.).
4 pecks = 1 busHel (bu.).
Hence 1 bu. = 4 pks. = 32 qts.
1. How much must I pay for 6 bags of oats, 2
bushels in a bag, at 50 cents a bushel?
2. I paid $10 for some bags of potatoes, 2 bushels
in a bag, at $1 a bushel. How many bags were
there?
3. If on returning the bags I receive 10 cents each,
how much will the potatoes actually cost me?
4. How many four-quart measures can be filled
with a bushel of corn?
5. If I give my hens 2 quarts of com a day,
how many days will a bushel last?
6. How many days will 6 bags of oats, two bushels
in a bag, last a horse if he eats 10 quarts a day on
the averse ?
7. If 2 quarts of salt are used in freezing 4 quarts
of cream, how many quarts of salt will be used in
freezing 4 gallons? How many pecks?
8. A man paid $2.50 for a load of sawdust con-
taining 25 bushels* What was the rate a bushel?
9. If 12 onions fill a four-quart measure, how
many onions of the same size will fill a bushel?
MBKTAL- ABITHMETIC. 67
XieMon 8.
1. How mQoh more will a peck of blueberries cost
at 10 cents a quart than at 75 cents a peck?
2. From a bushel basket of pears, three pecks are
sold. How many pecks remain ? How many quarts ?
3. If a bushel of peas in the pod make 4 quarts
when shelled, how many quarts will 3 pecks make ?
4. What must I pay for 4 bushels of potatoes at
75 cents a bushel ?
5. How many blackberries at 10 cents a quart
must be given for 2 books at 25 cents each ?
6. A boy receives 5 cents a bushel for picking
up potatoes. How many bushels must he pick up to
earn $1.26 ?
7. A farmer sells 2 bushels of Bartlett pears for
92, If he had to pay 25 cents a bushel for picking,
what is his profit ?
8. If a bushel of coal costs 25 cents, how many
bushels can be bought for $1.50 ?
9* A dealer buys beans at $2.50 a bushel, and
sells them at 10 cents a quart. How much does he
gain on a bushel ?
10. I paid 20 cents for a peck of salt. What was
the rate a bushel ?
U. At the rate of 5 cents a pint, what must be
paid for 2 quarts of peanuts?
12. Hulled corn is 6 cents a quart. How much
must I pay for 16 quarts ?
13. A boy buys a peck of popcorn for 60 cents,
pop« it, and sells it at 5 cents a bag. If he has 40
bags, how much does he make ?
&S MENTAL ABITHMETIC.
Lesson 9.
AVOIRDUPOIS WEIGHT.
Avoirdupois Weight is used in weighing all articles except
gold, silver, and precious stones.
Table.
16 ounces (oz.) = 1 pound (lb.).
2000 pounds = 1 ton (t.).
1. From 42 pounds of butter three lots of 12
pounds each are sold. How much is left?
2. I paid 20 cents a pound for a twenty-pound
firkin of butter. For how much a pound must I sell
it in order to gain $1?
3. At 25 cents a pound, what will 5 pounds of beef-
steak cost?
4. How much must I pay for 10 tons of coal at
$7.50 a ton ?
5. If hay sells at $20 a ton, what is the price of
one pound ? one hundred pounds ?
6. I bought hay at the rate of 80 cents a hundred.
What was the price of a ton ?
7. If a dealer buys 8 tons of coal for $32, and sells
it at 20 cents a bushel, 80 pounds to the bushel, how
much will he make ?
8. If it takes 5 bushels of wheat to make a barrel
of flour, how many bushels will it take to make 12
barrels of flour ? '
9. Is it cheaper to buy 4 quarter-barrels of flour
at $1.50 each, or a barrel for $5.50 ?
10. A bushel of potatoes weighs 60 pounds. What
will one peck weigh ?
MENTAIi ARITHMETIC. 69
Lesson 10. *
1. If 4 quarts of oats weigh 4 pounds, how much
will a bushel weigh ?
2. A grocer gives 20 lbs. of sugar for $1. What
is the rate a pound ?
3. At 60 cents a pound, how many pounds of tea
can be bought for $2 ?
4. If a pound of maple sugar would make a pint of
syrup, would it be cheaper to buy sugar at 12 cents a
pound, or syrup at $1 a gallon ? How much cheaper ?
5. If 12 candles weigh a pound, how much will
120 candles weigh ?
6. If 72 candles weigh 12 pounds, how many can-
dles will weigh 1 pound ?
7. A boy goes to the store with a five-dollar bill.
He buys a bag of sugar for $1, a pound of tea for 60
cents, a pound of soda for 10 cents, and a pound of
coffee for 40 cents. How many dollars has he left ?
8. How many pounds of sugar at 6 cents a pound
must be given for 8 dozen eggs at 25 cents a dozen?
9. How many tons of coal at $7.60 a ton can be
bought for 6 cords of wood at $6 a cord ?
10. If 1 bushel of oats weighs 32 pounds, what
would be the weight of a bag containing 80 quarts ?
11. How much must I pay for 2 chickens, each
weighing 3 pounds at 20 cents a pound?
12. Should I make more by selling a quintal of fish
(100 pounds) for $10, or at 11 cents a pound ?
13. Eight packages of equal weight are made of 4
pounds of tea. How many ounce? does each package
weigh ?
60 MBKTAL AmTHMSTXa
XiMflon 11.
TROT WmOHT.
Troy Weight is used in weighing gold, silver, and precions
•tones.
Tablb.
24 grains (grs.) = 1 pennyweight (dwt.).
20 pennyweights = 1 ounce (oz.).
12 ounces ^ 1 pound (lb.).
1. How many spoons weighing 20 pennyweights
each can be made from 10 ounces of silver ? From
1 pound ?
2. If an ounce of silver is worth 60 cents, what is
a pound worth ?
3. How many tablespoons weighing 3 ounces each
can be made from 6 pounds of silver ?
4. If 40 tablespoons of equal weight are made
from 10 pounds of silver, how many ounces will each
spoon weigh ?
5. If silver is worth 3 cents a pennyweight, what
must I pay for one ounce ?
6. If gold were worth $20 an ounce, what would
a pennyweight cost ?
7. How many pennyweights of silver at 3 cents
each would have to be given for 1 pennyweight of
gold worth 96 cents ?
8. If I buy gold dust at 2 cents a grain and sell it
at 50 cents a pennyweight, do I gain or lose ?
9. If in every ounce 15 pennyweights are silver
and the rest alloy, how many pennyweights are alloy
in a mug that weighs 10 ounces ?
HBNTAL ARITHMBTIO. 61
IiBMOll I?
IiONa MEA8URB.
Long Measure is used in measuring lines or distances.
Tablb.
12 inches (in.) =1 foot (ft.).
3 feet = 1 yard (yd.).
*6i yards, or 16^ feet = 1 rod (rd.). '
320 rods ^ 1 mile (mi.).
Hence, 1 mi = 320 rods = 1760 yds. = 6280 ft.
*NoTB. 5i is read five and a half .
1. In a coil of picture cord measuring 10 yards,
how many feet are there ? How many inches ?
2. My table measures 5 feet one way and 3 feet
the other. What is the distance round it ?
3. At the rate of two cents an inch, what will a
two-foot rule cost ?
4. What must I pay for 60 feet of border at 6 cents
a yard ?
5. How many yards of border will it take to go
round a- room 12 feet wide and 15 feet long ?
6. At $1 a yard what will be the cost of 5 strips
of carpet, each 5 yards long ?
7. What must I pay for 10 feet of galvanized pipe
at 14 cents a foot ?
8. Is it cheaper to buy a roll (10 yards) of tape
for 25 cents, or at the rate of 3 cents a yard ?
9. How many yards of cloth at $3 a yard must b^
given for 6 barrels of flour at $5 a barrel ?
10. If a man walks 4 miles an hour, how many
hours will it take him to walk 48 miles ?
62 ^ MENTAL ARITHMETIC.
Iiesson 13.
1. If concrete of the width of my walk costs 75
cents a yard, what must I pay for 10 yards ? ^
2. A lady buys 10 yards of dress goods at 60
cents a yard, and 20 yards of trimming at 5 cents a
yard ; if she gives in payment a ten-dollar bill, how
much change ought she to receive ?
3. At eight cents a foot, what will moulding cost
for a picture measuring 12 inches one way and 14
the other, allowing 8 inches extra for the corners ?
4. How many yards of fence ^ will be required for
a four-sided field measuring 33 feet one way and 66
the other ? What will it cost at $1 a yard ?
5. At 50 cents a yard, what must I pay for
curtains for a room containing 4 windows, each 2
yards long ?
6. A lady paid $48 for silk for a dress. If it
cost |!3 a yard, how many yards did she buy ? '
7. If a child steps one foot at each step, how many
steps will he take in walking a mile ?
8. What must I pay for 25 feet of rope for a
swing, at 4 cents a foot ?
9. At the rate of 2 cents a mile, how many miles
can I ride for $1 ?
10. If one page is 10 inches long, how many pages
placed in a row will extend 5 feet ?
11. At the rate of 15 cents a foot, what will it
cost me to lay a pipe from my house to the street,
a distance of 10 yards ?
12. It is 5 miles between two stations on a rail-
road. How many rods is it ?
MENTAL ABITHMETIC. 63
Lesson 14.
SQUARE MXSASURR
Square Measure is used in measuring surf a.ce8.
Table.
144 square inches (sq. in.) = 1 square foot (sq. ft.).
9 square feet = 1 square yard (sq. yd.).
•30i square yards, or I ^ ^ ^^ ^ ^ -^ ^
272J square feet )
160 square rods, or ) _ , , . >
10 square chains J - 1 acre (A.).
640 acres = 1 square mile (sq. mi.).
Hence, 1 A. = 160 sq. rds. = 4840 sq. yds. = 43,560 sq. ft.
* Note. 30^ is read thirty and a quarter.
1. Since there are 10 square chains in one acre,
how many acres are there in 50 square chains ?
2. At the rate of 5 cents a square foot^ what must
be paid for 100 square feet of boards ?
3. If a certain kind of flooring costs 20 cents a
square foot, how much will 20 square feet cost ?
4. Since 160 square rods make an acre and 10
square chains make an acre^ how many square rods
make a square chain ?
6. How many square feelT of wire screen can be
bought for 90 cents, at 2 cents a square foot ? How
many square yards ?
6. I paid a man $1.50 for mowing 2 acres of
grass. What was the rate per acre ?
7. If potatoes yield 75 bushels to the acre, how
many bushels ought a man to receive from 4 acres ?
8* How many lots of 40 square rods each can be
made from an acre ?
64
KBNTAL ARITHHETIO.
ZiMSOn 15.
The area of any surface is the nnmber of units of area the
given surface contains.
The unit of area is a square, the side of which is some given
unit of length.
Find the area of a rectangle 2 ft. by 8 ft :
The rectangle can be divided into 6 squares, each square
being 1 ft. on a side.
•
Therefore the area required is 2 x 3 sq. f t. = 6 sq. ft.
In finding the area of a rectangle :
We express the length and breadth in units of the same name,
and multiply the number of units in the length by the number of
units in the breadUi ; the product of these two numbers will be
the number of square unils qf that name,
1. What is the area o£ one side of an envelope
measuring 5 inches one way and 3 inches the other ?
2. What must I pay for leather at 12 cents a
square foot to cover the top of my desk, which meas-
ures 4 feet one way and 3 feet the other ?
3. If zinc sells for 10 cents a square foot, how
much must I pay for a* piece 6 feet long and 3 feet
wide to put under my stove ?
4. At the rate of 6 cents a square yard, what will
it cost to cover with sods a plot of ground 10 yards
long and 8 yards wide ?
5. How many square rods are there in a field 40
rods square ? How many acres ?
MENTAL AKITHMBTIO. 66
Iiesaon 16.
CUBIC BCBASURR
Cable Measure is used in measuring solids.
Tabus.
1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.).
27 cubic feet = 1 cubic yard (cu. yd.).
"WOOD BCQASURE.
Table.
16 cubic feet = 1 cord foot (cd. ft).
8 cord feet = 1 cord (cd.).
Therefore, 128 cubic feet = 1 cord.
1. Find the cost of 9 cords of wood at $6 a eord.
2. I paid $18 for a pile of pine wood, at the rate
of $3 a Gord; how many cords were there in the pUe ?
3. For how much a cord must I sell a pile of wood
containing 12 cords, that I may receive $60 ?
4. A pile of wood 4 feet high, 4 feet wide, and 8
feet long contains a cord. If a pile is 4 feet long and
4 feet wide, how high must it be to contain a cord ?
5. If it costs 25 cents to build a cubic foot of brick
wall, how much will it bost to build 8 cubic feet ?
6. If it costs 54 cents to dig a cubic yard of clay,
how much will it cost to dig a cubic foot ?
7. At the rate of 10 cents a cubic yard, a man
earned $20 for digging a cellar; how many cubic
yards did he dig ?
8. If a cubic foot of clay will make 10 bricks, how
many bricks can be made from a cubic yard ?
66 MENTAL ABITHMETIO.
Lesson 17.
VOLUMES.
The Tolttme of any solid is the nnmber of units of yolnme
the given solid contains.
The unit of volume is a cube, the edge of which is some given
unit of length.
In finding the volume of a rectangular solid:
We express the lengthy breadth, and thickness in units of the
same name ; then we multiply the number of units in the length
by the number of units in the breadth^ and this product by the
number of units in the thickneis ; the prodiu:t of these numbers
will be the number of cubic units of that name,
1. My inkstand measures 2 inches one way, 2 inches
another, and 2 inches another ; how many cubic inches
are there in it ?
2. Find the number of cubic inches in a brick 3
inches thick, 4 inches wide, and 8 inches long.
3. Find the number of cubic feet in a cake of ice
1 foot thick, 2 feet wide, 3 feet long.
4. What is the capacity of a coal bin 4 feet wide^
5 feet high, and 8 feet long ?
5. If a bunch of envelopes 5 inches long and 3
inches wide is 1 inch thick, how many bunches will
be required to make a pile containing 90 cubic inches ?
6. The capacity of a certain box is 100 cubic feet ;
one of the dimensions is 4 feet, another 5 feet. What
is the third ?
7. Find the capacity of a drawer 10 inches wide,
10 inches long, and 4 inches deep.
8. What is the volume of a mound of earth 12 feet
long, 10 feet wide, and 10 feet high ?
— -1
MENTAL ABITHMETIC. 67-
Lesson 18.
TIME MEASURE.
Time Measure is used in measuring duration.
Table.
60 seconds (sec.) = 1 minute (min.).
00 minutes = 1 hour (hr.).
24 hours = 1 day (dy.).
7 days = 1 week (wk.).
366 days (or 62 wks. 1 dy.)= 1 common year (yr.).
366 days = 1 leap-year.
100 years = 1 century.
1. Since there are 7 days in one week, how many
days are there in 12 weeks? How many weeks in 63
days ? in 84 days ?
2. If a man walks 20 miles a day, how far will he
walk in 3 days ? In 4 days ? In a week ?
3. If a train goes a mile a minute, how long will it
be going 60 miles?
4. If a boy earns $1 a day and spends 10 cents,
how much will he have left at the end of a week ?
5. If a man works 10 hours a day, how many hours
a day will be \eft for other things ?
6. How many minutes are there in 5 hours ?
7. If a working day is 8 hours, which is the better
rate, 20 cents an hour or $1.50 a day ?
8. A boy who picks 4 quarts of berries in an hour
has picked 12 quarts. How many hours was he picking?
9. If one ton of coal lasts a family two weeks, how
many weeks will twelve tons last? How many tons
will be required to last six months, reckoning four
weeks to a month ?
68 MENTAL ARITHMETIO.
IiMMiOn 19.
1. If a train runs 20 miles in 30 minutes, what is
its rate per hour ? How far will it run in 3 hours ?
2. If it takes a boy one minute to slide down a
hill and five minutes to walk up, how many times can
he slide down and return in an hour? In two hours ?
3. If it takes 2 men 3 days to do a piece of work,
how long will it take 1 man ? 3 men ?
4. If one man can do a piece of work in 30 days,
how long will it take 3 men? 6 men?
5. If a man can do a piece of work in 48 hours,
how many days will it take him, working 8 hours a
day? How many weeks, reckoning 6 working days ?
6. If a man walks 4 miles an hour and a horse
travels 8 miles an hour, how many miles will the
horse go while the man walks 12 miles?
7. If the interest of $1 is 4 cents a year, in how
many years will the interest be 48 cents ?
8. If a quantity of provisions will last 10 men 12
days, how long will it last one man ? 12 men?
9. How long will it take me to save $24, if I
save $2 a week ?
10. How many days are there in 9 weeks ?
11. If I walk 16 miles at the rate of 4 miles an
hour and without stopping ride back at the rate of 8
miles an hour, how long shall I have been gone ?
12. If 2 pipes will empty a cistern in 12 hours,
how long will it take 6 pipes of the same size to empty
it ? how long will it take 12 pipes ?
13. If 2 men can do a piece of work in 16 days,
how long will it take 4 men to do twice as much ?
MENTAL ARITHMETIC. 69'
LeBSon 20.
1. A bag of com meal weighs 100 pounds. How
many bags will weigh a ton ?
2. If a brick weighs 4 pounds, how many tons will
a load of 1000 bricks weigh ?
3. A score is 20. How many years old is a man
who is 3 score and 10 years old ?
4. A gross is 12 dozen. How many pens in a gross
of pens?
5. There are 24 sheets of paper in a quire and 20
quires in a ream. How many sheets are there in a
ream of paper ?
6. How many square rods in a house-lot 8 rods
front and 12 rods deep ?
7. If a rectangular lot has 10 rods front, what
must be its depth in order to contain an acre ?
8. If a box must have 5 cubic feet of space in order
to hold 4 bushels of oats, how many bushels will a
box hold that has 40 cubic feet of space ?
9. How many quarts in 10 gallons and 3 quarts ?
10. From a firkin of butter containing 27 pounds
8 ounces, 7 pounds and 4 ounces are sold. How much
is left in the firkin?
11. From a bushel of beans 4 quarts are sold.
How many 4-quart measures can be filled from the
beans that are left ?
12. How many cubic feet in a box that measures
inside 3 feet long, 3 feet wide, and 3 feet high ? How
many cubic yards ?
13. How many cords of wood in a pile 16 feet long,
4 feet wide, and 4 feet hij^h?
CHAPTER III.
FRACTIONS.
Lesson 1.
1. Into how many equal parts is the apple di-
vided?
2. What is the name of each part ?
3. The name, one-half, tells that the whole apple
is divided into how many equal parts ?
4. How many halves of an apple make 1 apple ?
5. If the square contains 10 sq. ft., how many square
feet are there in one-half of it ?
6. If a man walks 4 miles in an hour, how far will
he walk in one-half of an hour ?
7. How many cents are there in one-half of a dol-
lar ?
8. How many inches are there in one-half of a
foot ? one-half of 2 feet ? one-half of 6 feet ?
9. How many ounces are there in one-half of a
pound ? one-half of 4 pounds ?
10. How many halves can be made from 1 cake ?
3 cakes ? 7 cakes? 11 cakes ?
11. How do we express one-half with figures ?
MENTAL ARITHMETIC. 71
ZiOSflon 2.
1. What part of a quart is one pint ?
2. How many quarts are there in 4 pints? 12
pints ? 20 pints ? 24 pints ?
3. How many dollars are there in 2 half-dollars ?
6 half-dollars ? 10 half-dollars ? 18 half-dollars ?
4. If 18/ pears are divided equally between two
boys, what part of 18 pears will each boy receive ?
5. If one-half of a pound of copper costs 6 cents,
what is the cost of a pound ?
6. Six is i of what number ?
7. James has 7 dollars and John has 12 half-
dollars. How much more has James than John ?
8. By what number must 8 be divided to get ^ of 8 ?
9. What is i of 14? 18? 26? 80? 100?
10. If a ten-quart pail is half full of water, how
many quarts of water are in the pail ?
11. If you have five apples of the same size, how
can you divide them equally between two boys ?
12. How many quarts are there in one-half of a
bushel ? How many quarts in ^ of a half -bushel ?
13. How many half-dollars make 2 dollars? 2^
dollars ? 3^ dollars ? 4^- dollars ?
Solution T One dollar is equal to 2 half-dollars. Therefore 2
dollars are equal to 2 x 2 half-dollars, or 4 half-dollars ; and 2^
dollars are equal to 4 half-dollars and 1 half-dollar, or 5 half-
dollars.
14. How many half-bushel measures will 2^
bushels of wheat fill ? will 5^ bushels fill ?
15. If oate are put up in bags of 2^ bushels in
a bag, how many bushels will there be in 2 bags ?
72
imrTAI- ABITHICaiXC.
\
M
/
/
^
\
%
%
%
*A
1. Into how many equal parts is the circle divided ?
2. What is the name of each part ?
3. The name, one-fourth, or one-quarter, tells that
the whole circle is divided into how many equal
parts ? How many fourths in the whole circle ?
4. How many quarters are there in 1 dollar ?
. 5. If a square contains 16 sq. ft., how many square
feet are there in one-fourth of it ? in two-fourths ?
6. How many marbles are there in one-fourth of
8 marbles ? 12 marbles ? 20 marbles ? 32 marbles ?
36 marbles ? 40 marbles ?
7. How many gills are there in one-fourth of a
pint? in one-fourth of a quart? one-fourth of 4
quarts ?
8. How many ounces are there in one-quarter of a
pound? in two-quarters of a pound? in three-quar-
ters ? in four-quarters? in one pound and a quarter ?
9. How many eggs are there in one-fourth of a
dozen of eggs? in two-fourths? in one-half? in
three-fourths ? in one dozen and a quarter ?
10. How do we express one-fourth, or one-quarter,
with figures? two-fourths? three-fourths?
11. How many more eggs in ^ of a dozen than in
^ of a dozen ? How many fourths make one-half ?
XieHKm4.
1. How many quarters of an apple are there in
one-Half of an apple ? in two halves of an apple ?
2. How many halves of an apple are there in two-
fourths of an apple ? in four-fourths ?
3. What part of a bushel is 1 peck ? 2 pecks ? 3
pecks ? 4 pecks ?
4. How many quarters of an apple can bd made
from 1 apple? 3 apples? 6 apples? 12 apples?,
5. If four men hire a carriage and the charge is
9Sy what part of $8 should each man pay to divide
the expense equally?
6. If boards cost $20 a thousand feet, what is the
cost of ^ of a thousand feet ? of f of a thousand feet ?
7. By what number do we divide 20 to find one-
fourth of 20 ?
8. What is i of 16? 24? 40? 48? 100?
9. What is i of $8 ? i of $4? i of $2 ?
10. 92 is i of what ? $1 is i of what ?
11. How many quarters of a dollar are there in
$1 ? in $2 ? in $2i ? in $2^? in $3i ?
12. How many bushels of oats will there be in 2
bags if each bag contains 2^ bushels ? How many
bushels will there be in 4 bags ?
13. How many fourths are there in i and ^ to-
gether ?
14. If from a pile of quarters of a dollar you take
3 quarters each time for 4 times, how many dollars
will you have ?
15. How many whole ones in 4 times ^? in 4
times f ? in 4 times | ? in 4 times i ?
74
MENTAL ABITHMETIC.
ZiesionS.
H
'A
V»
1. Into how many equal parts is the pineapple
divided ?
2. What is the name of each part ?
3. The name, one-third, shows that the whole is
divided into how many equal parts ?
4. How many thirds of the circle in the whole
circle ?
5. If the rectangle contains 15 sq. ft., how many
square feet are there in one-third of it? in two-
thirds ? in three-thirds ?
6. If 12 boys are arranged in 3 groups so that
there is the same number of boys in each group,
what part of the whole number of boys is in each
group? How many boys are there in each group?
What part of 12 is 4 ?
7. How many feet are there in one-third of a
yard ? two-thirds of a yard ? one-third of 2 yards ?
8. How do we express one-third with figures?
two-thirds ? three-thirds ?
9. How many oranges will be required to give
each of 12 boys \ of an orange? ^ of an orange?
\ of an orange?
10. Which is greater, \ of an orange or ^ of an
orange? ^ of an orange or ^ of an orange?
MENTAL ABITHMETIC. 75
Iieaaon 6.
1. If 2 apples are divided equally among 3 boys,
what part of an apple will each boy receive ?
Hmt. Each apple must be divided into 3 equal parte, and
each boy will have 2 of these parte, or } of 1 apple.
2. If ^ of a barrel of flour costs $2, what is the
cost of a barrel of flour ?
3. 2 is J of what number ? 3 is ^ of what number ?
4. If § of a ton of hay cost $12, what is the cost
of ^ of a ton ? what is the cost of a ton ?
5. How many square feet are there in ^ of a
square yard?^ in f of a square yard ?
6. What part of a yard is 1 foot? 2 feet?
7. How many yards are there in 6 ft. ? in 9 ft. ?
in 24 ft. ? in 27 feet ? in 30 feet ?
8. How many inches are there in J of a foot? in
J of a yard? in f of a foot? in J of a yard?
9. By what number do you divide 12 to find J of
12? What is J of 15? 21? 30? 36? 63? 90?
10. If Frank has lost ^ of his money, how many
thirds' has he left ? If he had $12 at first, how many
dollars did he lose ? how many dollars has he left ?
11. How many more oranges are there in |- of a
dozen than in ^ of a dozen ? in ^ of a dozen than in
^ of a dozen ? in -^ of a dozen than in ^ of a dozen ?
12. How many minutes are there in 1 hour and i
of an hour ? in 1 hour and f of an hour?
13. If you take i of the pine-apple, how many
thirds will be left ? if you take f, how many thirds
will be left ? What then is 1 — i ? 1 — f ?
76
lOBHTAL ▲BITHMBTIC
7.
h
%
H
M
H
H
1. Into how many equal parts is the circle divided ?
2. What is the name of each part ?
3. How masij sixths of the circle make the whole
circle ?
4. If the square contains 18 sq. ft., how many
square feet are there in one-sixth of it? in three-
sixths? in five-sixths?
5. How do we express one-sixth in figures ? five*
sixths? three-sixths?
6. If 12 books are divided equally among 6 boys,
what part of the 12 books will each boy receive ?
7. How many months are there in ^ of a year, in
•J of a year ? in ^ of a year ? in J of a year ?
8. How many sixths of a year in ^ of a year? in
J of a year? in f of a year?
9. If Frank received ^ of 18 marbles and Charles
i of 18 marbles, how many marbles did both receive ?
10. If Henry has ^ of 30 peaches and John has ^
of 30 peaches, how many peaches have both?
11. One-half of 30 is equal to how many sixths of
80 ? "i^ of 30 is equal to how many sixths of 30 ?
12* What part of anything is 2 times |- of it? 3
times i of it ? 4 times | of it ?
HEXTAL AHITHMBTIC. 77
IiesBon 8.
1. How many inches are there in J of a foot? in
J of a foot? in ^ of a foot ? in f of a foot ? in ^ of a
foot ? in I of a foot ? in f of a foot ?
2. How toany minutes are there in J of an hour ?
in i of an hour? in f of an hour? in f of an hour ?
3. Four-sixths of an hour is equal to how many
thirds of an hour ?
4. If a man works six days each week, what part
of a week's wages will he earn in 1 day? in 2 days?
in 3 days? in 5 days ? in 4 days ?
5. If four pies are divided equally among some
boys 80 that each boy receives ^ of a pie, how many
boys are there?
6. By what number do you divide 12 to get ^ of 12 ?
7. Whatis Jof 18? 24? 30? 42? 64? 60?
8. 8 is ^ of what number ? 9 is ^ of what number?
9. How many square feet are there in ^ of a mat
9 feet long and 4 feet wide?
10. How many square inches are there in | of a
board 12 inches long and 3 inches wide?
11. If ^ of a pound of rice costs 2 cents, what is
the cost of 1 pound ? of 6 pounds ?
12. If you divide ^ of an apple into 2 equal parts,
what part of the whole apple will each of these two
parts be ? What then is ^ of i? iXi?
13. If you divide ^ of an apple into 3 equal parts,
what part of the whole apple will each of these parts
be ? What then is^of^? iXi?
14. How many sixths in i? in -J-? in^+^? in
i~-i? in2Xi? in2Xi?
78
MENTAL ABITHMETIO.
Leflson 9.
1. Into how many equal parts is the circle di-
vided?
2. What is the name of each part ?
3. How many fifths of the circle in the circle ?
4. If a square contains 10 sq. ft., how many square
feet are there in one-fifth of it ? in three-fifths ?
5. If a pie is divided equally among 5 boys, what
part of a pie will each boy receive ?
6. What will be the share of each boy if 3 cakes
are divided equally among 5 boys ?
7. How do we express one-fifth with figures ? two-
fifths ? three-fifths ? four-fifths ? five-fifths ?
8. If Frank had 15 pears and gave away J of them,
how many pears did he give away ? How many
fifths had he left ? How many pears had he left ?
9. A farmer had 10 bushels of wheat. He sold ^
of his wheat to one man and } of his wheat to an-
other man. How many bushels did he sell ?
10. If it costs $7 to dig ^ of a ditch, what will it
cost to dig the whole ditch ?
11. 7 is J of what number? 9 is ^ of what num-
ber ? 11 is ^ of what number ?
MENTAL ABITHMETIG. 79
Lesaon 10.
1. If 2 pounds of copper can be bought for ^ of a
dollar, how many pounds can be bought for a dollar ?
2. By what number do you divide 30 to get J of
30?
3. What is J of 25 ? 35? 50? 75 ? 100 ?
4. What is the sum of J of 20 and J of 20 ?
5. Thomas had 30 marbles. If he lost ^ of them
and gave away } of them, how many fifths had he
left ? How many marbles had he left ?
6. What is the difference between ^ of 30 and ^
of 30? ^of 30 audi of 30?
7. 8 is f of what number ?
Solution : If 8 is } of a number, ^ of the number will be ^
of 8, or 4. If 4 is i of the number, f of the number will be 6
times 4, or 20. But f of a number is the number itself, there-
fore, 8 is I of 20.
8. 12 is } of what number ? 12 is J of what num-
ber ? 12 is J of what number ?
9. If you have 25 cents and spend f of your
money, how much money will you have left ?
10. If you spend f of your money, how many
fifths will you have left ?
11. What is f of 25 ? f of 25 ? | of 25?
12. 24 is } of what number ? 24 is f of what num-
ber ? 24 is ^ of what number ?
13. How many fifths are J+i? * + *? i + i?
*-i? *-»? *-f^ 2Xi? 2X*?4Xi? iof I?
iofj? ioff?
14. How many fifths in 2 ? in2|? in3|? in4i?
in6f? in8|?
80
MENTAL ARITHMETIC.
Zieason 11.
/\y»
KyA
\>i
%/
1 yz\
/^ \
^ \
/^
\ ^/
\% 1
%X
\ ji
\^H
%\/
Xh
^ \
1. Into how many equal parts is the circle divided ?
2. What is the name of each part ?
3. How many eighths of the circle in the circle ?
4. If a square contains 24 sq. ft., how many square
feet are there in one-eighth of it ? three-eighths ?
four-eighths ? seven-eighths ? eight-eighths ?
5. How many ounces in one-eighth of a pound ?
in two-eighths of a pound ? in :J of a pound?
6. One-fourth is equal to how many eighths ?
7. How many quarts are there in one-eighth of a
peck ? in four-eighths of a peck ? in ^ of a peck ?
8. One-half is equal to how many eighths ?
9. How do we express one-eighth with figures ?
three-eighths ? five-eighths ? seven-eighths ?
10. A gill is what part of a pint ? of a quart ?
11. How many gills are there in | of a quart ?
12. If one-fourth of a pound of oil is mixed with
1^ of a pound of turpentine, how many ounces will
the mixture weigh ?
13. If Mary found 2 dozen eggs and broke \ of
them, how many eighths had she left ? How many
eggs did she break ? How many eggs had she
left?
MENTAL ABITHMETIC. 81
IieBson 12.
1. If Charles can hoe f of a field in a day and
Joseph can hoe ^, how many eighths can both hoe in
a day ? in 2 days ? How many days will it take
them to hoe the field ?
2. How many quarts are there in ^ of a bushel ?
3. By what number do you divide 32 to find ^ of
32?
4. What is ^ of 24 ? 40 ? 56? 72? 80 ?
5. If it costs $20 to build | of a wall, what will it
cost to build ^ of it ? to build the whole wall ?
6. 20 is I of what number ?
7. How many eighths in ^ ? in |^? in f ?
8. How many eighths in i and ^ ? in J and ^ ? in
i and i and | ? in ^ and f ? in J and f ?
9. ' If you have -J^ of a bushel of cranberries and
sell J of them, what part of a bushel have you left ?
10. How much is ^ of ^ ? i of i?
11. How many eighths in 1 ? in 1^? in 2f ?
12. How many ounces in ^ of a pound ? in f of a
pound ? in f of a pound ? in If pounds ?
13. How many quarts in ^ of a bushel ? in f of a
bushel ? in f of a bushel ? in J of a bushel ?
14. Since 1 is equal to |, how much is 1— f ?
1-f? 1-i? 1-i?
15. James had 40 chickens. He lost f of them ;
how many had he left ?
16. How many eighths are2Xi? 2Xf? ^off?
iof|?ioff? ioff?iof|?
17. After spending 50 cents I have f of my money
left. How many cent9 tod I at first ?
82
MENTAL ABITHMETIG.
laeMon 13.
T»ff
tV
A
tV
A
tV
tV
A
■At
iV
1. Into how many equal parts is the rectangle
divided ?
2. What is the name of each part ?
3. How many tenths of the rectangle make the
whole rectangle?
4. If the rectangle contains 40 sq. ft., how many
square feet are there in one-tenth of it ? two-tenths ?
three-tenths ? five-tenths ? seven-tenths ? •
5. How do we express one-tenth with figures ?
three-tenths? seven-tenths? nine-tenths?
6. How many cents are there in -j\y of a dollar ?
7. Four ten-cent pieces make how many tenths of
a dollar ? seven ten-cent pieces ?
8. How many hundredweight are there in ^ of a
ton ? ^ of a ton ? J of a ton ?
9. One-fifth of a ton is equal to how many tenths
of a ton ? Two-fifths is equal to how many tenths ?
10. How many minutes are there in ^ of an hour?
-j^ of an hour ? i- of an hour ? |^ of an hour ?
11. One-half of an hour is equal to how many
tenths of an hour?
12. If a yard of silk costs $1, what will a yard
cost if ^ of the price is takeu off ?
MENTAL ABITHMETIC. 83
IiesBOQ 14.
1. If 3 cakes are cut into tenths^ how many boys
can be supplied with ^ of a cake ?
2. If a man gives away ^ of a basket of peaches
and sells ^, how many tenths are left ?
3. Thomas was given a half-dollar to spend. If
he spent ^ of it for cherries and ^ of it for a pencil,
how many tenths did he spend ? How many cents did
he spend ? How many cents had he left ?~
4. If it costs $15 to paint -^ of a house, what is
the cost of painting ^ of the house ? How much
will it cost to paint the house?
5. 15 is ^ of what number ?
6. What is ^V of 40? 60 ? 70? 90 ? 100 ?
7. 4 is ^ of what number ? 4 is ^ of what num-
ber ? 4 is 3^ of what number ?
8. 6 is ^ of what number ? 8 is -j^^ of what num-
ber ? 10 is ^'^f of what number ?
9. 30 is ^ of what number ? 30 is ^ of what
number ? 30 is ^ of what number ?
10. 66 is ^jf of what number ? 66 is ^ of what
number ? 64 is ^ of what number ?
11. Whatisiof i? ioii? ^of A? ioi^? iot^?
12. What part of 10 is 1? 2? 3? 7? 9?
13. How many tenths in ^ + y\y ? in ^ + tV ^ ^"
i-^V? in*-TV^ iri2X:,\? m2X^? in2XT^?
in3XA? in^of A? iniof^^? in^of^V?
14. How many times is ^ contained in i^ ? in
^%? inT7^? inV^? inV\,?
15. How many more rods are there in ^ of a mile
than in -j]^ of a mile ? Which is greater, then, iV ^^ i ^
84
MENTAL ARITHMETIC.
laesflon 15.
1. Into how many equal parts is the rectangle
divided?
2. What is the name of each part?
3. The name^ one-twelfth, tells that the whole
rectangle is divided into how many equal parts ?
4. How many twelfths of the rectangle make the
whole rectangle ?
5. If the rectangle contains 48 sq. ft., how many
square feet are there in one-twelfth of it? five-
twelfths? six-twelfths? nine-twelfths?
6. How do we express one-twelfth with figures?
five-twelfths? seven-twelfths?
7. How many inches are there in <,i^ of a foot ? in
^ of a foot? in ^ of a foot ? in ^ of a foot ? in -j^
of a foot ? in J of a foot ? in j\ of a foot ?
8. One-half of a foot is equal to how many twelfths
of a foot? how many sixths of a foot? how many
fourths of a foot ?
9. How many buttons are there in t^ of 2 dozen
buttons ? i of 2 dozen ? J of 2 dozen ? J of 2 dozen ?
10. One-third of 2 dozen is equal to how many
twelfths of 2 dozen ? how many sixths of 2 dozen ?
11. If twelve pence make a shilling, how many
pence are there in -^ oi & shilling? J of a shilling?
12. One-fourth of a shilling is equal to how many
twelfths of a shilling ?
MENTAL ARITHMETIC. 85
LOBSOn 16.
1. One-sixth of a dozen is equal to how many
twelfths of a dozen?
2. How many months are there in ^ of a year?
J of a year? f of a year? ^ of a year? J of a year ?
J of a year? | of a year? {^ of a year?
3. What part of a foot are three inches ? 4 inches ?
6 inches? 11 inches? 9 inches ? 8 inches ?
4. How many minutes in i of an hour? J of an
hour ? J of an hour ? ^\y of an hour? ^ of an hour ?
5. By what number do you divide 60 to get ^J^ of 60 ?
6. What is tV of 36 ? 48? 72? 96? 120?
7. If V\r of an acre of land cost $15, what is the
cost of ^ of an acre ? of an acre ?
8. Two is ^ of what number ? 10 is ^ of what
number ? 14 is /^ of what number ?
9. How much is ^ of J ? i of i? i of ^? i of t^?
10. How many twelfths make 1?2?3?6?7?
11. What part of 12 is 2? 3? 4 ? 5 ? 6? 8? 9?
12. If eggs cost 24 cents a dozen, what is the cost
of 1^ of a dozen ? ^ of a dozen ? ^ of a dozen ?
13. What is T^ of 36 ? 48? 84? 96? 60?
14. i is equal to how many twelfths ? ^ is equal
to how many twelfths ? J is equal to how many
twelfths ? i is equal to how many twelfths ?
15. How many twelfths in ^ + t^ ? in i+ iV ^ ^^
i + T^? mi-j\? ini-T^,? ini-T-V? in3XxV?
in4XT^j? in6XT^? in^of V\r? in^ofyv?
16. How many more minutes in y\y of an hour
than in ^^ of an hour ? Which is greater, then, y\y
or tV ?
86 MENTAL ARITHMETIC.
Lesson 17.
1. How many eighths are there in J ? in J ? in J ?
in I? in J? in 1 and'^? in 1 andj? inland^?
2. How many tenths are there in J? in J? in §?
in J? in f ? in 1 and t^? in 1 and J? in 1 and J?
3. How many twelfths are there in J ? in J? in § ?
in J? in I? in J? in |? in f ? in|? in|?
4. Which is greater, ^ ov fy? Jor^? i or fy?
5. How many ten-cent pieces make J^ of a dollar?
6. A rug is 9 ft. long and its width is ^ of its
length. How wide is it? How many square feet
does it contain ?
7. If the width of a hall is \ of its length and its
width is 5 ft., what is its length? How many square
feet are there in its floor ?
8. If the surface of a floor contains 60 sq. ft., how
many square feet are there in J of it ? J of it ? J of
it? J of it? i of it? tV of it? ^ of it? § of it?
f of it ? i of it ? I of it? ^jf of it ? fy of it ?
9. If a 12-gallon keg is § full of syrup, how many
gallons does it contain ?
10. What is the sum of J of 15 and J of 15?
11. If 24 peaches are divided so that Charles re-
ceives I of them and Henry the rest, how many more
will Henry receive than Charles ?
12. How many more minutes in } of an hour than
in J of an hour ?
13. Into how many equal parts must a ship-
wrecked crew divide their provisions, so that they
may have enough to last a week? What part of the
whole will be consumed in 3 days ?
MENTAL ASITHMETIC. 87
Ziesson 18.
What is tlie name of one of the parts when any-
thing is divided into :
1. 2 equal parts ? 7. 8 equal parts ?
2. 3 equal parts ? 8. 10 equal parts ?
3. 4 equal parts ? 9. 12 equal parts ?
4. 5 equal parts ? 10. 16 equal parts ?
5. 6 equal parts ? 11. 36 equal parts ?
6. 7 equal parts ? 12. 100 equal parts ?
A cake can be cut into how many :
13. Halves? 21. Tenths?
14. Thirds? 22. Elevenths?
15. Fourths? 23. Twelfths?
16. Fifths? 24. Sixteenths?
17. Sixths? 25. Twentieths?
18. Sevenths? 26. Twenty-fifths?
19. Eighths? 27. Thirty-sixths?
20. Ninths? 28. Hundredths?
When anything is divided into 12 equal parts,
what do we call :
29. 1 part? 32. 4 parts? 35. 8 parts?
30. 2 parts ? 33. 5 parts ? 36. 10 parts ?
31. 3 parts? 34. 6 parts? 37. 12 parts?
38. Three melons were divided among some boys.
If the first was cut into fourths, the second into
sixths, and the third into eighths, how many boys
could receive one piece of melon ?
39. How many boys can receive a piece of pie if 4
pies are divided into fifths ?
88 MENTAXi ABITHMBTIC.
Iiesson 19«
Any standard used in counting, or measuring, is called
a unit. One book and one dozen of eggs are examples of units
used in counting. One foot and one pound are units used in
measuring.
Units are either whole units or equal parts of whole units ;
as one orange, one-fourth of an orange.
A unit which is one of the equal parts of a whole unit is
called a fractional unit ; numbers used in counting fractional
units are called fractions ; and numbers used in counting whole
units are called integers, or integral numbers.
Name the fractional unit and the whole unit of
which it is a fraction in the following expressions :
1. J of an apple. 7. | of a dollar.
2. I of an inch. 8. § of a foot.
3. -j^r of a rod. 9. \i of a pound,
4. I of a pie. 10. J of an ounce.
5. ^xs o^ ^ dollar. 11. ^ of a peck.
6. I of a yard. 12. J of a mile.
The upper number of a fraction is called the numerator, or
number-giver; as it gives the number of fractional units taken.
The lower number is called the denominator, or name-giver; as
it gives the name of each part. The numerator and denominator
are called the terms of the fraction.
Write in figures :
13. five sixths. 17. two seventeenths.
14. three sevenths. 18. seven fiftieths.
15. nine elevenths. 19. eleven eightieths.
16. ten twentieths. 20. thirteen hundredths.
21. Read : f , ^^, ^, J|, H, r,% ^\, ^%.
MENTAL ABITHMETIC. 89
Lesson 20.
Ex. 1. What is the meaning of | yd ?
The denominator shows that the unit, one yard, is divided
into 6 equal parts, and the numerator 6 means that 6 of these
parts are taken.
Ex. 2. What is the meaning of | standing alone ?
The denominator 4 shows that the unit, whatever that unit
is, is divided into 4 equal parts, and the numerator 3 means
that three of these fourths are taken.
In the same way what is the meaning of :
1. |lb? 5. fA?
9.
i yd ? 13.
^5?
2. f bu. ? 6. $f ?
10.
^j rd. ? ■ 14.
A?
3. Jqt.? 7. «i?
11.
i gal. ? 15.
A?
4. ^cd.? 8. ItVit?
12.
^js ton ? 16.
it?
What is the value of ;
17. f lb. in oz. ?
27.
f t. in cwt. ?
18. f ft. in in. ?
28.
1 cd. in cd. ft.
?
19. $^ in cents ?
29.
il yd. in in. ?
20. i cwt. in lb. ?
30.
^*y bu. in qt. ?
21. /^ hr. in min. ?
31.
1 mi. in rd. ?
22. i mi. in rd. ?
32.
§ cu. yd. in cu.
ft.?
23. i yd. in ft. ?
33.
§ sq. yd. in sq.
ft.?
24. f yd. in in. ?
34.
J sq. yd. in sq.
ft.?
1
25. 1 gal. in pt. ?
35.
I cu. yd. in cu.
ft.?
26. } pk. in qt. ?
36.
1 A. in sq. rd.
9
•
37. If a farmer's wife makes 25 lb. butter a week
and sells ^ of it, how many pounds does she sell ?
38. If a boy has 5 eggs, how many more does he
need to make | of a dozen ?
90 MEI^TAL ARITHMETIC.
LeBBon 21.
1. What kind of a measure will ^ of a gallon fill ?
^ of a gallon ? ^ of a gallon ?
2. If Joseph can hoe his cornfield in 6 days, what
part can he hoe in 1 day ? in 2 days ? in 5 days ?
3. If a boy has gone J of the distance to school,
how many fifths of the distance remain ?
4. If an ounce of silver costs $f , what is the cost
of 10 ounces ?
5. If building f of a wall costs $15, what is the
cost of building J of it ? J of it ? of building the
whole wall ?
6. What is the sum of J of 12 and J of 20 ?
7. Charles has 13 marbles and John has 18. How
many will each have if John gives i of his marbles
to Charles ?
8. A purse contains 16 quarters of a dollar and
there are 50 ten-cent pieces in a box. Which con-
tains more money ? How much more ?
9. If a painter charges $1 for ^ of a day's work,
what is his charge for a day ? for 6 days ?
10. Henry Jones sold a sleigh which cost $40 for
I of its cost. How many dollars did he lose ?
11. If 7 men earn $28, what part of $28 does 1
man earn ? 5 men ?
12. Paul had 30 apples and divided | of them
among 6 boys. How many did each boy receive ?
13. If eggs are worth 3 cents apiece, what is the
cost of I of a dozen of eggs ?
14. What is the whole unit in f of a dofeen ?
15. How many sevenths in the whole of anything ?
MENTAL ARITHMETIC. 91
Lesson 22.
A mixed number consists of a whole number and a fraction ;
as 2}, read two and three-fourths.
A proper fraction is a fraction whose numerator is smaller
than its denominator ; as {.
An improper fraction is a fraction whose numerator is not
smaller than its denominator ; as ^, |.
Name the proper fractions, the improper fractions,
and the mixed numbers of the following :
h \h h h 3i, 2§, 7i, f , I, *, #, Jj/i, 5J, ii, V, 8J,
¥. hh A> Hh ¥. A> ¥. 8§> ¥. A. A. V> ^i, 7f ,
Ex. 1. How many dollars are there in 8 quarters ?
Since 4 quarters make one dollar, there will be as many dol-
lars in 8 quarters as there are 4^s in 8 ; that is, 2 dollars.
Ex. 2. How many dollars are there in 9 quarters ?
Since 4 quarters make one dollar, there will be as many dol-
lars in 9 quarters as there are 4's in 9 ; that is, 2 dollars and 1
quarter over, or 2^ dollars.
1. How many yards in ^ yd. ? in ^ yd. ?
2. How many bushels in J bu. ? in } bu. ? in ^-
bu. ? in Ji^ bu. ? in ^- bu. ? in V- bu. ? in ^^ bu. ?
3. How many pounds in ^ lb. ? in i^ lb. ? in
V- lb. ? in If lb. ? in |J lb. ?
4. How many dollars in $ y ? in $ \<i ? in $ J^ ?
in $^? in $^^? in $^J-? in $^? in Iv?
5. How many units and what part of another unit
in Y? in-y? inV? ii^V"? inV"^ inV? in V^
in^yi? inff ?
92 MENTAL ARITHMETIO.
ZaesBon 23.
How many units are there in :
1. ^Ah,? 6. ^? 11. fj? 16. y?
2. J^in.? 7. '^a? 12. 5^? 17. :ff?
3. ^:^bu.? 8. ^? 13. ^^? 18. ft?
4. V^t-? 9- ¥^ 14- ¥? 19- ¥?
5. ^ it? 10. V-^ 15- ¥? 20. ^?
21. How many bushels of peaches are there in 27
baskets, if each basket contains ^ bu. ?
22. How many gallons will be required to fill 18
bottles, if each bottle holds J gal. ?
23. How many pounds of tea will be required to
make 36 half-pound packages ?
24. A merchant has 35 packages of cream of tar-
tar, each containing \ lb. How many pounds of
cream of tartar has he ?
25. A boy has 25 quarters of a dollar. How
many dollars has he ?
26. If a man's steps average | ft., how many feet
long is his step ?
27. If a house is ^ yd. long, how many yards
is the length of the house? How many feet?
28. If a barrel holds ^ bushels of apples, how
many bushels does the barrel hold?
29. If ^ gal. of water fill a barrel, how many
gallons does the barrel hold ?
30. If a pail contains ^ qt. of water, how many
quarts does it contain ? How many pint bottles can
be filled from the pail?
31. How many dozens of bananas in ^ doz. ?
MENTAL ARITHMETIC. 93
Lesson 24.
1. How many half-dollars are there in $3 ? $4 ?
$7? $10? $15? $25?
2. How many quarters are there in $1, $5, $11 ?
3. How many half-dollars are there in $3 J ? $5^ ?
4. How many quarters are there in $1J? $2|?
$5J? $10f?
5. How many fifths are there in 3 ? 8 ? 13 ? 3f ?
9i? 5i? 6i? lOi?
6. How many sixths are there in 2? 5? 9? 15?
3J? 3|? 4J? 8i?
7. How many sevenths are there in 1 ? 3 ? 7 ?
11 ? 2f ? 5^ ? 8f ? 12| ?
8. How many eighths are there in 5 ? 6 ? 9 ? 10 ?
IJ? 2|? 7|? 8i?
9. How many ninths are there in 2? 7? 11?
12? Si? 4J? 5f ? 6f?
10. How many tenths are there in 5 ? 8 ? 11 ?
16? 5tV? 7t^? V,r? l<Mr? ^tV?
11. How many ten-cent pieces should a man re-
ceive for $2 J ?
12. If 6 apples are divided equally among some
boys so that each boy receives J of an apple, how
many boys are there?
13. John cut 8 apples into thirds and Frank cut
7 apples into quarters. How many more pieces had
Frank than John ?
14. A man has $3} in quarters, how many quar-
ters has he ?
15. How many cents are there in $3 ? $4 ? $5 ?
$2i? $3J? $1J? $2t^? H^jj?
94 MENTAL ARITHMETIC.
ZaesBon 25.
1. A cook has five cakes. How many more pieces
will she have, if she cuts them into sixths, than if
she cuts them into quarters ?
2. If a cook gives a quarter of a cake to each of 7
boys, how many cakes must she cut?
3. If a string is 3} yards long and another string
is 2\ yards long, how many more quarters of a yard
are there in the length of one than of the other ?
4. The distance between two windows is 1§ yd.
How many times must a foot rule be applied to
measure the distance?
5. There are 16} ft. in a rod. How many times
must a half-foot rule be applied to measure a rod ?
6. A grocer puts up 32 lb. of tea in } lb. packages.
How many packages does he make?
7. What will 7} yd. of silk cost, if i yd. costs $1 ?
8. How many eighths of a pound in 6} lb. ?
9. How many pint bottles can be filled with 18}
quarts of water?
10. How many quarts are there in 7| pecks?
11. How many stones will be needed to pave a
walk containing loj sq. ft., if the upper surface of
each stone contains J sq. ft. ?
12. How many blocks containing J cu. ft. will fill
a space containing 9 j cu. ft. ?
13. In 4 J how many halves ? fourths ?
14. In 5| how many fourths? eighths?
15. In 6§ how many thirds? sixths?
16. In 4| how many fifths? tenths?
17. In 2| how many sixths? twelfths?
MENTAL AUITHMETIC. 95
' ZaesBon 26.
1. How many quarters of a dollar in $i ?
2. How many halves are there in J? |? }? J^?
Changing f to ^ we call reducing | to its lowest terms. A
fraction is in its lowest terms when no whole number, except 1,
will divide both its terms without a remainder.
3. How many sixths of an apple in ^ of an apple ?
4. How many thirds are there inf? J? f? \ft?
5. How many eighths of a peck in ^ pk. ?
6. How many fourths are there inf? J? |? ^?
7. How many tenths of a dollar in $ J ?
8. How many fifths are there in y^ ? ^ ? t^^ ? t% ?
9. How many twelfths of a dozen in J doz. ?
10. How many sixths in ^J^j? ^? ^%? /j? jj?
11. How many sixths of an orange in ^ of an
orange ?
12. How many halves in | ? | ? y ?
13. Which is greater, J or f ? ^y or i? {$ ov i?
fori? JJor§?
Express in lowest terms :
14.
i-
20.
A-
26.
\i-
32.
\i-
38.
§«•
15.
}•
21.
A-
27.
A-
33.
u-
39.
if.
16.
I-
22.
A-
28.
A-
34.
if-
40.
!*•
17.
t-
23.
A-
29.
H-
35.
A-
41.
90
10 0-
18.
f-
24.
V-
30.
A-
36.
it-
42.
A'lr-
19.
A-
25.
V-
31.
A-
37.
if
43.
A\f
44. What part of a pound are 6 oz. ? 12 oz. ?
Note. — In all examples we reduce the answers to their sim-
plest form, by reducing fractions to their lowest terms and
changing improper fractions to whole or mixed numbers.
96 MENTAL ARITHMETIC.
LesBon 27. *
1. What is the product of 5 times 3 books ?
2. What is the product of 5 X 3 fourths ?
3. What is the product of 5 X f ?
4. What is the product of7XJ?llXf?8X|?
12XTfir? 5Xli? 4X§? 6X/3? 9XV?
5. What is the produ^ct of 6 X f ? of f X 6 ?
Solution : 6 X ^ = 5 or f ; therefore 6 x | = 5 x | = y, or 3f .
6. What is the product of 7 X ^^^ ? of ^^ X 7 ?
7. Find the product of 5 X t^. 6 X ^, 8 X f .
12 Xf 4XJ. 5Xt^. 7X^5. 3XH- ^ X tV
8. How many ounces are there in J lb. ? | lb. ?
9. How many pounds are there in J of 100 lb. ?
10. How many quarts are there in J bu. ? | bu. ?
11. How many dollars in 16 X $f ?
12. How many years in § of a century ?
What is the product of :
13.
2X|.?
26.
f Xl6?
39.
!ftrof6?
14.
3X|?
27.
§ X 16?
40.
^oi20?
15.
3x5?
28.
iJX5?
41.
f of 36 ?
16.
15X§?
29.
■ft X7?
42.
f of 36 ?
17.
12xf?
30.
i>„X8?
43.
^, X 15 ?
18.
8X|?
31.
f X9?
44.
rxv^?
19.
7X^?
32.
■ftxio?
45.
VkX24?
20.
4XH?
33.
S of 16 ?
46.
T»y X 14 ?
21.
SXt^j?
34.
A of 24 ?
47.
3XA?
22.
8xyi?
35.
>?5 of 6 ?
48.
21Xt^?
23.
f X3?
36.
/v of 6 ?
49.
24X1?
24.
§X12?
37.
iiofS?
50.
30 X|?
25.
^X12?
38.
|of 9?
51.
lOOXif^?
MENTAL ARITHMETIC. 97
ZaesBon 28.
1. How many pints of vinegar will be required to
fill 24 bottles each containing ^ of a pt. ?
2. What is the cost of 18 yd. of muslin at $} a
yard ?
3. How many quarts in |^ of a bushel of berries ?
4. If Henry can dig ^ oi 2l ditch in 1 day, what
part of the ditch can he dig in 15 days ?
5. If the hour-hand moves ^ of the distance
around the dial in 1 hour, what part of the dial
will it move over in 9 hours ?
6. How many yards of ribbon will be needed to
make 40 bows, each containing f of a yard ?
7. If a pump delivers f of > quart at each stroke,
how many quarts will be delivered by 32 strokes ?
8. If 15 lb. of sugar can be bought for $1, what
part of a dollar is the cost of 1 lb. ?
9. How many quarts of coffee will be needed to
give each of 36 men a cup containing J pt. ?
10. What is the cost of 42 lb. of scrap iron at ^
of a cent a pound ?
11. If a furnace consumes J of a ton of coal a day,
how many tons will it consume in 30 days ?
12. How many square rods are there in ^ A, ?
13. How many minutes are there in f of an hour ?
14. How many quarts of milk will be needed to
supply 12 families, if each family uses 2J quarts ?
15. If a horse eats 4§ quarts of corn in 1 day,
how many quarts will he eat in 15 days ?
16. If Henry is 20 years old and Charles is f as
old, what is the sum of their ages ?
98 MENTAL ARITHMETIC.
Lesson 29.
1. What is the product of 2X3? of2Xi? What
then is the product of 2 X 3^ ?
2. What is the product of 3X6? of3Xf? What
then is the product of 3 X 6§ ?
3. What is the product of 4X7? of4XJ? What
then is the product of 4 X 7J ?
4. What is the product of 6X5? of6XJ? What
then is the product of 6 X 5J ?
5. What is the product of 5x3j? 7X6|?
4x6i? 3JX6? 10JX8? 3X9J?
Note. — In the following examples count a fraction of a cent
a whole cent, as is usually done.
What is the cost of :
6. 3^ doz. eggs at 16 cents a dozen ?
7. 4 J lb. of tea at 50 cents a pound ?
8. 4^ lb. of sugar at 6 cents a pound ?
9. 8 cans of tomatoes at 12^ cents a can ?
10. 8 lb. of ham at 15^ cents a pound ?
11. 5\ lb. of bacon at 16 cents a pound ?
12. 2^ lb. of steak at 23 cents a pound ?
13. 2J lb. of cheese at 18 cents a pound ?
14. 5^ lb. of halibut at 15 cents a pound ?
15. 2f lb. of coffee at 36 cents a pound ?
16. 3| yd. of velvet at $4 a yard ?
17. 12 lb. of copper at 10 J cents a pound ?
18. 8J yd. of cotton cloth at 6 cents a yard ?
1^- 5§ yd. of cotton cloth at 8 cents a yard ?
20. 12 lb. of nails at 2} cents a pound ?
21.' 8| gal. of vinegar at 20 cents a gallon ?
MENTAL ABITHMETIC. 99
Lesoon 30.
1. If a man walks 3 miles an hour, how far will
he walk in 3 J hours ?
2. What is the railway fare for 22 miles at 2^
cents a mile?
3. What is the weight of 4 gal. of milk at 7} lb.
to the gallon ?
4. What is the weight of 3J cu. ft. of dry white
pine at 25 lb. for each cubic foot ?
5. What is the weight of 1 J cu. ft. of dry white
oak at 52 lb. a cubic foot ?
6. If cork weighs 15 lb. per cubic foot, what will
5J cu. ft. weigh ?
7. If a cubic foot holds f of a bushel, how many
bushels will a bin hold if it contains 15 cu. ft. ?
8. If a bushel equals H cu. ft., how many cubic
feet will be required to hold 18 bushels ?
9. If a man earns $2j a day, how much will he
earn in 12 days ?
10. If Joseph rows 3| miles in an hour, how far
can he row in 4 hours ?
What is the cost of :
11. 2f acres of land at $40 an acre ? j
12. 28 rods of fence at $3^ a rod ?
13. 6J tons of hay at $15 a ton ?
14. 16 yards of carpet at $1^ a yard ?
^ 15. 30 cords of wood at $3§ a cord ?
16. If 6 men can mow a field in 2^ hours, in how
many hours can one man do the work ?
100 MENTAL ARITHMETIC.
Lesson 31.
1. How many inches are there in 4 J ft. ? 3 J ft. ?
2. How many quarts are there in 3| gal. ? 6^
gal. ? 2J gal. ?
3. How many ounces are there in 1| lb. ? 5 J lb. ?
1| lb. ? 4^5 lb. ?
4. How many hundredweight are there in IJ t. ?
2J t. ? 3f<j t. ? IJJ t. ?
5. How many eggs are there in 2§ doz. ? 3J doz. ?
Ij doz. ? 7 J doz. ? 2|J doz. ?
6. How many feet are there in 5 J yd. ? 7§ yd. ?
7. How many cubic feet are there in IJ cu. yd. ?
8. How many square feet are there in 2 J sq. yd. ?
9. How many quarts are there in 1^ pk. ? 3^ pk. ?
10. What is the cost of a ton of steel at 1^ cents
a pound ?
11. A farmer bought a cow for $36 and sold her
for IJ times the cost. What was the selling price ?
How many dollars did he gain ?
12. If an average hill of potatoes contains | of a
peck, how many bushels will 48 hills contain ?
13. If a square rod of land produces 1| bu. of
potatoes, how many bushels will J of an acre pro-
duce ?
14. If a man hires some money agreeing to pay
$1J for every dollar borrowed, how much should he
pay if he borrows $48 ?
15. What is the cost of 6 dozen cans of peas at
$1| a dozen ?
16. If a boy picks If quarts of berries in an hour,
how many quarts can he pick in 5 hours ?
MENTAL ARITHMETIC. 101
Lesson 32.
1. What is J of J, or J X J ?
2. What is the product ofJXJ? JX|?§X|?
3. What is the product of ^%Xi?
4. What is the product of^XV^ ofJtj^Xf?
What is the
product
of:
5. §Xt?
13.
fXA?
21.
/tjX^?
6. |X|?
14.
iXii?
22.
Axv?
7. ?X8?
IS.
}X/r?
23.
Aof>V«?
8. |Xf?
16.
«X}g?
24.
Aoffl?
9. ?X-V»?
17.
iX^?
25.
f of V- ?
10. 1 X ^ ?
18.
fiXH?
26.
§ofy?
11. §X??
19.
|x§t?
27.
fof J^?
12. |Xf? 20. -/^Xll? 28. fiofif^
29. If the fuel for a furnace costs $f a day, what
is the cost for f of a day ?
30. A man owning ^ of a vessel sold J of his
share. What part of the whole vessel did he sell ?
31. If a field produces $ of a bale of cotton, what
part of a bale will ^ of the field produce ?
32. If a pulp mill uses J of a cord of spruce in
1 hour, what part of a cord will it use in J of an
hour ?
33. A lot containing \^ of an acre was divided
equally among 5 people. What part of an acre did
each receive ? How many square rods ?
34. If J of the population of a town is less than
21 years old and | of those under 21 attend school,
what part of the whole population attends school ?
102 MENTAL ARITHMETIC.
LeflBon 33.
Note. When we multiply a mixed number by a fraction,
we generally change the mixed number to an improper frac-
tion, and then proceed to multiply.
What is the product of :
1. fXU? 9. tVof5i? 17. T^,yX2f?
2. fXlf? 10. ?of4|? 18. 4|XJ?
3. iX2|? 11. ioflyi,? 19. 50Xyi^?
4. ^Xl§? 12. iof3?? 20. iof3J?
5. iX2i? 13. HXli? 21. |of4i?
6. j\X3i? 14. 2iXl|? 22. Aof6i?
7. fofl^? 15. 3JX|? 23. iftjofej?
8. |oflJ? 16. IJXl?? 24. T»rOf5i?
What is the cost of :
25. S\ yd. of silk at $2^ a yard ?
26. 2^ yd. of silk at $1^ a yard ?
27. 2^ yd. of satin at $1J a yard ?
28. 3^ doz. cans of peaches at $3^ a dozen ?
29. 3^ doz. cans of tomatoes at $1^ a dozen ?
30. 2^ thousand shingles at $2| a thousand ?
31. 1^ cords of wood at $3f a cord ?
32. 2i tons of coal at $4| a ton ?
33. 3| bu. of wheat at $1} a bushel ?
34. 2^ bu. of beans at $2^ a bushel?
35. 2f thousand feet of gas at $1^ a thousand ?
36. 3} bundles of clapboards at $2^ a bundle ?
37. 2i kegs of nails, at $2J a keg ?
38. A man bought 3 lb. of mutton at 15f cents a
pound and 2^ lb. of cheese at 14 cents a pound.
What change should he receive for $1 ?
MENTAL ARITHMETIC. 103
LeMon 34.
What is the cost of :
1. 3i bu. of salt at $f a bushel ?
2. The car fare for 36 miles at 2^ cents a mile ?
3. 7 cans of peas at $} a can ?
4. 3 lb. of pork at 12^ cents a pound ?
5. 9 cans of cherries at $^ a can ?
6. 12 bushels of corn at $f a bushel ?
7. 3^ quarts of blueberries at 15 cents a quart ?
8. f of a flock of 14 sheep, if 1 sheep costs $6 ?
9. 2 lb. 12 oz. of butter at 24 cents a pound ?
10. How many yards are there in 2 rods ? 5 rods ?
11. How many feet are there in 2 rods ? 4 rods ?
12. If a man earns $lf a day, how much will he
earn in 7^ days ?
13. If a man walks 3^ miles in an hour, how far
will he walk in IJ hpurs ?
14. Allowing H lb. for each man, how many
pounds of beef will be needed for 10 men. ?
15. If a furnace consumes If tons of coal in a
month, how many tons will it consume in 3^ months ?
16. How many minutes are there in | of an hour ?
17. How many yards are there in ^ of a rod ?
18. If a box of oranges costs $4^, what is the cost
of -J- of a box ?
19. If a man owned |^ of a vessel and sold f of his
share, what part of the vessel did he sell ?
20. If a bushel of hard coal weighs | of a hundred-
weight, how much will 20 bushels weigh ?
21. If a bushel of soft coal weighs ^^ of a hun-
dredweight, how much will 20 bushels weigh ?
104 MENTAL ARITHMETIO.
LesBon 35.
1. If a man has $4 in $1 bills, how many bills
has he ? If he has $4 in half-dollars, how many
half-dollars has he?
2. If dividing 4 by 1 means finding how many
ones there are in 4, what is the meaning of 4 divided
by ^ ? How many halves are there in 4 ?
3. How many halves are there in 6 apples ? What
then is the quotient of 6 -f- -J- ?
4. How many thirds are there in 2 pies ? What
then is the quotient of 2 -^ -J- ?
5. How many quarters are there in $3? What
then is the quotient of 3 -5- i ?
6. Among how many boys can 4 apples be divided,
if each boy receives J of an apple ? J of an apple ?
7. What is the quotient of 4 -5- f ?
8. If a cook has 3 cakes, to how many girls can
she give J of a cake ? f of a cake ?
9. What is the quotient of 3 -=- f ?
10. What is the product of 3 multiplied by J ?
11. If a man has 4 melons, to how many boys can
he give i^ of a melon ? f of a melon ?
12. What is the quotient of 4 -^ f ?
13. What is the product of 4 multiplied by | ?
14. If 3 divided by f is the same as 3 multiplied
by J, and 4 divided by | is the same as 4 multiplied
by |, then 6 divided by § is the same as 6 multiplied
by what fraction ?
Hence, in dividing by a fraction
We invert the fraction and multiply the dividend by
the inverted fraction.
MENTAL ABITHMBTIC.
105
Leuon 36.
What is the
quotient of
1. 6-i
Hf?
7. 12 -i
-i?
13.
6-j-^?
2. 6-
■^v
8. 12 H
H§?
14.
8-5-f?
3. 9-H
-F
9. 12-^
rf?
15.
9-*-f ?
4. 10-
Hf?
10. 12-
^f?
16.
16-f-l?
5. 12 H
-i?
11. 15-
-1?
17.
7-^ A?
6. 12-
i- 1?
12. 10-^
^«?
18.
12-f-lf?
19. At $f a yard how many yards of flannel can
be bought for $6? for $10 ? for $16 ? for $24 ?
20. At $^ a gallon how many gallons of molasses
can be bought for $6 ? for $7 ? for $9 ? for $11 ?
21. At $J a can how many cans of peas can be
bought for $3 ? for $3^ ? for $3^ ?
22. At f of a cent a pound how many pounds of
scrap-iron can be bought for 20 cents ?
23. At $^|^ a pound how many pounds of writine
paper can be bought for $12 ?
24. If a boy earns $f a day, how many days will
it take him to earn $9 ?
25. If a man can build | of a rod of wall in 1 day,
in how many days can he build 10 rods ?
26. If f of a barrel of flour is worth $2, what is
the value of ^ ? of | ?
27. If it costs $6 to mow f of a field, what is the
cost of mowing the whole field ?
28. Six is § of what number ?
29. Philip agreed to pay f of the cost of hiring a
boat for 2 weeks. If his share was $6, what was
the whole cost?
30. What is the quotient of 6 -f- f ? ,
106
MENTAL ABITHMETIC.
LeBBon 37.
1. What is the value of4^f? off-4-f?
2. What is the value of f X J ?
3. Is f multiplied by J the same in value as f ~ J ?
4. How many yards of cloth at $J a yard can be
bought for $^ ?
5. How many pounds of beef at f ^ a pound can
be bought for $f ?
6. At $^ a can how many cans of peas can be
bought for $i ?
7. If Peter can pick a quart of berries in f of an
hour, how many quarts can he pick in § of an hour ?
8. If 1 man can slate ^^ of a roof in 1 day, how
many men can slate ^ of it in 1 day ?
9. If Joseph has f of a melon, to how many boys
can he give J of a melon ?
10. To how many girls can a cook give -j^ of a
cake, if she has | of a cake ?
11. If A owns y^ of a vessel and B owns ^, how
many times B's share is A's share ?
12. How many pounds of crackers at $^ a pound
can be bought for f 2^ ?
13. How many pounds of coffee at 9f a pound
can be bought for $1^?
What is the quotient of : ^
14. fH
-*?
20. -i^H
-A?
26. t-i
-A?
15. i-i
hi?
21. /j^
-1?
27. f-i
-A?
16. fH
rf?
22. T^jH
-1?
28. l-i
-A?
17. f-^
-t?
23. 1^5 -^
rj?
29. f-
i-H?
18. |H
-§?
24. A.
-f?
30. i-^
-t'f?
19- t'«
-J?
25. T»5-
l-f?
31. f-i
Mi?
MEKTAL ABITHHETIC.
107
Leaaon 38.
1. How many halves are there in 1^ ?
2. What is the quotient of 6 -j- f ?
3. What then is the quotient of 6 -$- 1^?
4. In 2^ how many halves? In 1^ how many
fourths ?
5. What is the quotient of f -5- 1 ?
6. What then is the quotient of 2^ -f- 1^ ?
7. What is the quotient of 4-^2? of i-4-2?
8. What is the value off-i-3? offXi?
9. Is I -s- 5 the same in value as | X ^?
What is the quotient of :
10. 12-f-lJ? 20. f-5-10?
11. 12-4-11? 21. i-i-H?
22. l|^3i?
23. 3i-^f?
24. 3i-j-lJ?
25. li-^l?
26. 3i-5-li?
27. 4i-s-li?
28. 2iH-li?
29. 4f-4-31?
40. At $li a yard how many yards of cloth can
be bought for $3^ ? for $4^ ?
41. At $2| a cord how many cords of pine wood
can be bought for $7 '!
42. At $4^ a ton how many tons of coal can be
bought for $18 ?
43. At $2f a bushel how many bushels of beans
(;an be bought for $8 ?
12. 10-5-li?
13. 16-s-lf?
14. 8-f-lf?
f-s-12?
f H-8?
f-5-3?
|H-12?
#-5-10?
IS.
16.
17.
18.
19.
30. lf-f-2i?
31. 2^-f-l^?
32. li-5-2^?
33. 2TJ5H-li?
34. 2i-i-3i?
35. li-5-6?
36. 2iH-i?
37. lt\,-5-i?
38. 2j-^2f?
39. 3i-^2i?
108 MENTAL ARITHMETIC.
Lesson 39.
1. What is the sum of 1 half and 1 half ? 1 third
and 1 third ? i and i? i and f ?
2. What is the sum of i + f ? i+f ? i + f?
^ + «? fXf? % + i? ^ + ^+^?
What is the sum of :
3.
* + f + l?
9.
^^f + ^'^ + ^^T?
4.
l+i+l?
10.
A + A + T^?
5.
i+l+f?
11.
f+?+f ?
6.
#+i+f?
12.
f + f + t?
7.
i+i+i?
13.
tV + A + A?
8.
Vb + A + T^^?
14.
I+V + V ?
15. What is the sum of 1^+ If +2-J? 2i+f+li?
16. What is the sum of If + 2f +3^ ? 2^ + 5^^
17. Jane had J of a cake and gave away f . How
many fifths had she left ?
18. A man having \^ of a bushel of oats sold ^
of a bushel. How many sixteenths had he left ?
What is the remainder of :
19. I-I? 23. ^-V-? 27. H-A?
20. I- J? 24. H~t\? 28. H-^iy?
21. f-l? 25. H-i??? 29. H-A*^
22. f~f? 26. H-/^? 30. ii-^j?
31. What is the value of 2| — 2^ ? 3f — IJ ?
32. What is the value of 3f — 1^ ? oi 6J — 2| ?
33. What is the value of i + i— i? i + f — i?
* + J-f? f+f-f? l + ^-«?
34. What is the value of f—i + J? J — f +i?
MENTAL ARITHMETIC. 109
LesBon 40.
1. ^ equals how many fourths ?
2. How many fourths are there in ^ + J?
3. i equals how many sixths ?
4. How many sixths are there in i+ J ?
5. -J- equals how many sixths ?
6. How many sixths are there in ^+|^ ?
7. How many sixths are there in^+f? i + |?
8. i equals how many twelfths ?
9. i equals how many twelfths ?
10. How many twelfths are there in i+ J? f +i ?
f+i? i+i? i+i?
11. How many eighths are there in i+i? ^+i?
*+i? i+f ? i+i? i + f ? i + i + i?
12. How many sixths are there in i + i + J ?
i+f + i? i + i + i?
13. How many tenths are there ini^+-j^? J+-^'i*
l+A? f + A? 4+A? *+^? i+i? i+i+iV?
Note. Since we cannot add units that are not alike, frac-
tions that have different denominators must be changed to equi-
valent fractions of the same denominator before they can be
added or subtracted.
14. How many fourths are there in^— J? J — f?
15. How many sixths are there in -J- — ^? f — f?
' 16. How many twelfths are there in i — ^?
i— .V? i— iV? i— rV? H-f? fir-i? i-i?
17. How many tenths are there in^ — ^? i — ^?
A-i? i—h"^ *-/ir? A-f? i-i? l-i?
18. How many sixteenths are there in i — -j^ ?
i-A? i-A? i-A? 4— I'lr? H-i? «-i?
110 MBNTAL ARITHMETIC.
LeMon 41.
What is the
sum of :
1- *+*?
6. i+l?
11.
4+§+l?
2. i+i?
7. 4+??
12.
1+4+*?
3. l+i?
8. i+i?
13.
4+i+iV?
4. i+i?
9. i+f?
14.
f+4+Vk?
5. i+i?
10. i+J?
15.
4+?+A?
16. Philip can hoe ^ of a field in 1 day and James
can hoe J. What part can both hoe in 1 day ?
17. Thomas can dig f of a ditch in 1 day and
Henry can dig ^. What part can both dig in 1 day ?
18. Robert caught a trout weighing i lb. and
George caught one weighing f lb. What would both^
together weigh ?
19. From a stick ^^ of a foot long |^ of a foot is
cut off. What part of a foot is left ?
20. Frank was given a sum of money. He spent
i of it for books, ^ of it for a hat, and ^ of it for car
fares. What part of it did he spend ?
21. Mary picked J of a bushel of blackberries,
Sarah f of a bushel, and Helen ^^ of a bushel.
What part of a bushel did they all pick ?
22. If a pipe can fill a tank in 6 hours, what part
can it fill in 1 hour ? If a second pipe can fill the tank
in 4 hours, what part of the tank can it fill in 1
hour ? What part can both fill in 1 hour ?
23. If one pipe can fill a tank in 4 hours and a
second pipe can empty it in 5 hours, what part of the
tank will be filled in 1 hour, if both pipes are open ?
24. What is the weight of a mixture of f lb. of
alcohol^ f lb. of linseed oil, and ^ lb. turpentine?
MENTAL ABITHMETIC. Ill
Lesson 42.
What is the remainder of :
1. 1-f ? 3. 1-f? 5. 1-A? 7. 1-A?
2. 1-i? 4. 1-A? 6. l-T^^? 8. 1-H?
9. To make a whole unit what fraction must be
added to i? f ? f ? f ? VV? A? *? T^xF? «? i?Tr?
10. What improper fraction. is equal to l + -j\y?
1+*? l+A? i+T^i? lA? 1^? li^? IH?
11. What improper fraction is equal to 2 — ^?
3-f ? 2-J? 4— f? 5—1? 6— i? 3-f ? 2 — J?
12. How many pounds of beef will be left after
J lb. are cut from a piece weighing 3 lbs. ?
13. A man building a wall finished J of it the
first day, and ^ of it the second day. What part of
the wall was still unfinished ?
14. If ^^ of a pole is under water and the rest is
above water, what part is above water ?
15. If 1^ of the ice in an ice-house has melted and
f of it has been sold, what part remains ?
16. A and B shingle -J- of a roof in 1 day. A
shingles ^ of it, what part does B shingle ?
17. A and B can dig a trench in 6 days. What
part can they dig in 1 day ? If A can dig ^ of it
in 1 day, what part can B dig in 1 day ?
18. A can mow a field in 5 days. His son can
work only half as fast. What part can the son mow
in 1 day ? What part can both mow in 1 day ?
19. If A can dig a ditch in 3 days, B in 4 days,
and C in 6 days, what part can the three dig in 1
day ? What part will remain at the end of 1 day ?
112 MENTAL ARITHMETIC.
Lesson 43.
Ex. What is the sum of 2f + 3 J + 4| ?
Solution: i + f-f S = T«jf+r\ + i8 = H = 2i.
24-84-4 + 2i=lli.
What is the sum of :
1. lf + 3i? 6. H+2i + n?
2. 3f + lV>^? 7. 2i+2|+3i?
3. 2f + 2J? 8. Si + liV + Wij?
4. 2^ + 3^^? 9. 7i+5i+4|?
5. 3i + 4t? 10. 6f + 8j + 10i?
11. A grocer bought 7^ bu. of potatoes from A,
3f bu. from B, and 8| bu. from C. How many
bushels did he buy from the three ?
12. A coal dealer sold 2^ tons of coal to one man,
4 J- tons to a second, and 6^ tons to a third. What
was the weight of the three sales ?
13. A target for testing cannon was made from a
steel plate If ft. thick, with a backing of oak 4^ ft.
thick. What was the thickness of the target ?
14. If a boy weighing 70f lb. rides a bicycle
weighing 20f lb., what is the weight of both ?
15. A man earns $3 J in a day and his son $1^ a
day. How much do both earn in a day ?
16. A plumber worked 7f hours on Monday and
8^ hours on Tuesday. How many hours did he work ?
17. A and B start from the same spot and walk
in opposite directions. If A walks 3f miles an hour
and B 2f miles an hour, how far apart will they be
at the end of an hour ?
18. What is the sum of 2 ft. 8 in. and 6 ft. 9 in. ?
MENTAL ARITHMETIC. 113
Zieaaon 44.
Ex. 1. What is the difference between 2f and 1^ ?
Solution : i~i = f — } = i;and2 — 1 = 1. Therefore the
difference is 1^.
Ex. 2. What is the difference between 4J and 2| ?
Solution : 4f - 2| = 4/j - 2^ = 3^ - 2|§ = l|i, Ans.
What is the remainder of :
1. 3t-lA?
8.
6i-4i?
2. 6-2f?
9.
5f-4i?
3. 6i-3i?
10.
3M-2}?
4. 7-6f?
11.
4j-3i?
5. 4|-2i?
12.
6A-2t?
6. 6i-3|?
13.
3,^-21?
7. 6f-3i?
14.
8t«ij-4A?
15. If 2|- quarts are taken from a gallon of vinegar,
how many quarts remain ?
16. If from a piece of cloth containing 16|- yd.
m yd. are sold, how many yards are left ?
17. If a man's income is $23^ a week and his
expenses are $18f a week, how much does he save in
a week ?
18. If a man spends § of his salary for board and
^jf of it for other expenses, what part does he save ?
19. A piece of cloth measured 12f yd. before
sponging and 11| yd. after sponging. How much did
the cloth shrink ?
20. A pipe delivered 16^ gal. into a tank, but 4^
gal. leaked out. How many gallons remained ?
21. Mr. Smith owns 3 small farms containing 8f ,
10^, and 12J acres. How many acres does he own?
114 MENTAL ABITHMBTIG.
LeflBon 45.
Ex. 1. What fraction of 7 is 3 ?
Solution: Since 1 is ^ of 7, 3 is3 x i of 7, or f of 7.
Ex. 2. What fraction of*^ is i?
Solution : Since i = | and ^ = f , | is the same part of J that
2 is of 3, or |.
1. What part of a pound are 4 oz. ? 8 oz. ? 6 oz. ?
2. What part of a foot are 9 in. ? 6 in. ? 8 in. ?
3. What part of a yard are 2 ft. ? 1^ ? 2^ ft. ?
4. What part of a yard are 12 in.? 18 in. ? 8 in. ?
6. What part of a mile are 80 rd. ? 40 rd. ?
6. What part of a gallon are 2 qt. ? 2^ qt. ?
7. What part of a bnshel are 8 qt. ? 24 qt. ?
8. What part of an hour are 5 min. ? 10 min. ?
15 min. ? 30 min. ? 45 min. ? 60 min. ?
9. At $20 a ton what part of a ton of hay can be
bought for $6 ? $10 ? $15 ? $8 ? $12 ?
10. At $6 a cord, what part of a cord of wood can
be bought for $3 ? $4? $li?
J.1. At $7 a ton what part of a ton of coal can be
bought for $3i? $2^? $lf? $8f? $10^?
12. How many pounds are there in ^ of 100 lb. ?
f of 100 lb. ? I of 100 lb. ? J of 100 lb. ?
13. What fraction of 100 is 12^ ? 37^ ? 62^ ? 87^ ?
14. How many pounds are there in ^ of 100 lb. ?
J. of 100 lb. ? i of 100 lb. ? f of 100 lb. ?
15. What part of 100 is 8^? 16f ? 33^? 66f ?
16. What part of 100 is 20 ? 40 ? 25 ? 75 ? 175 ?
17. If a horse costing $100 was sold at a loss of
$16f , what part of the cost was the loss ?
MENTAL ARITHMETIC. 115
IieBSon 46.
374-
Ex. Keduce r^ to a simple fraction.
Solution: Multiply both terms by 2, and we have ^jj,
which reduced to its lowest terms is |.
Reduce to a simple fraction in its lowest terms :
,16} 62J 2^
100 100 100
100 '' 100 100
100 **• 100 100
.834 18f 28J
100 ^' 100 100
5 12* 31i lli
^ 100 "^"- 100 "moo
16. A suspended bank pays its depositors at the
rate of 66|- cents for each dollar deposited. What
part of his deposit will each depositor receive ?
17. If the average decrease in the value of the
machinery of a factory is 12^ cents on a dollar eiwjh
year, what part is lost each year ?
18. If each dollar invested pays a man 8-J- cents a
year, what part of his whole capital invested is re-
turned to him each year ?
19. If a vessel is insured so that 33J cents will be
paid to the owners for every dollar of cost, for what '
part of the cost is the vessel insured ?
20. If 14i^ lb. of a mass of metal weighing 100
lb. are copper, what part of the whole is copper ?
116 MENTAL ARITHMETIC.
LesBon 47.
1. If a yacht sails 6f miles in an hour, how many
miles will it sail in J of an hour ? in 2 J hours ?
2. If some plums are divided equally among 7
boys, what part of the whole will 5 boys receive ?
3. A field is 20 rods long and 8 rods wide. How
many square rods are there in -^ of the field ?
4. Mr. Brown sold a carriage for J of its cost and
received $60. What was the cost of the carriage ?
5. 60 is J of what number ?
6. 42 is f of what number ?
7. 22 is ^ of what number ?
8. If a pound of copper costs 9f cents, what will
2 pounds cost ? f of a pound ? 2f pounds ?
9. How many 6-cent pieces make ^^ of a dollar ?
10. How many pounds of soda will be required to
make 30 quarter-pound packages ?
11. If f yd. of velvet costs $1, what is the cost of
1 yd. ? of 9 yd. ?
12. A man being asked his age replied that he
had lived 2f score years. How old was he ?
13. If a cubic foot contains | of a bushel, how
many bushels will a bin hold if ijb is 4 ft. long, 3 ft.
wide, and 2^ ft. deep ?
14. How many cubic feet in 12 bu. ? 30 bu. ?
15. If 5 men can hoe a cornfield in 4^ hours,
how long will it take 1 man to hoe the field ?
16. If spruce costs $2^ a cord, what will be the
cost of 3^ cords ?
17. If a vessel is divided into 16 shares, what part
of the vessel belongs to a man owning 3^ shares ?
UKSTAL ABITHMBTIC. 117
Lesson 4&
1. A trader sold a load of hay for { of its cost
and gained 96, What was the cost of the load ?
2. A and B start from the same place at the same
time and walk in the same direction. If B walks 3^
miles per hour and A walks 2f miles per hour, how
far apart will they be in 1 hour ? in 6 hours ?
3. How far apart will A and B be in 5 hours, if they
walk in opposite directions at the rate given in Ex. 2 ?
4. A floor is 12 ft. long and 8 ft. wide. What is
the cost of tiling f of it at $1 per square foot ?
5. If it costs $48 dollars to build a fence, what
part of the fence can be built for $8 ? *20 ? $32 ?
6. If 12^ cents of every dollar received by a mer-
chant is profit, what part of his receipts is profit ?
7. If 20 cents of every dollar received is profit, the
gain is what part of the cost ?
8. What part of the dial of a clock does the hour-
hand move over, while the minute-hand goes once
around the dial?
9. What part of the dial will the hour-hand move
over while the minute-hand is going f of the distance
around the dial ?
10. If the minute-hand moves 30 minute spaces,
how many does the hour-hand move in the same time ?
11. A owns ^ of a factory and B owns | of it.
What part of B's share is A's share ?
12. If 18 weavers earn $27 in a week, what part
of $27 will 4 weavers earn ?
13. If a man's wages average $1.66f a day, what
part of $1 does he earn in a day ?
118 MENTAL ARITHMETIC.
Lesson 49.
1. A farmer raised 12j tons of hay and sold f of
it. How many tons did he sell ?
2. A farmer sold ^ of his flock of sheep and kept
20 sheep. How many had he at first ?
3. If ^ of a yard of ribbon costs 16 cents, what is
the cost of f of a yard ?
4. A man walked from Boston to New Haven in
8-J- days. What part of the distance did he walk in
2i days ?
5. A can shingle ^^ of a roof in a day. How
many days will it take him to shingle the roof ?
6. B can paint a house iri 6f days. What part can
he paint in 1 day ?
7. A and B can mow a field in 8 hours and A can
mow it in 12 hours. How long will it take B work-
ing alone to mow the field ?
8. If a monthly magazine costs at the rate of 16f
cents a copy, what is the cost for 1 year ?
9. If a man saves 37^ cents a day, how long will
it take him to save f 3 ?
10. If a boy earns $i a day and spends f f a day,
how much can he save in 12 days ?
11. If a unit is divided into 15 equal parts, what
name do you give to one part ?
12. How many house lots each containing ^^ of
an acre are there in a field containing 14 acres ?
13.. A dressmaker in making a dress uses 12f yd.
of silk, 6i yd. of lining material, and 2^ yd. of
velvet. How many yards are used in making the
dress?
MENTAL ABITHMETIG. 119
LeBBon 50.
1. What is the cost of 5i doz. jars at $f a dozen ?
2. What part of f^r is f ? of f is f^ ?
3. A man owning -^^ of a factory gave his share
to his 5 children. If an equal division is made what
part of the factory will each child receive ?
4. If a man earns $lf a day and his son earns $f
a day, how much more will the father earn than the
son in 1 day? in 4 days?
5. If C can build a wall in 9 days and D in 7 days,
what part can each do in 1 day ? in 3 days ?
6. A man owning f of a ship sells f of his share
for $4,000. What is the value of the ship ?
7. How many feet are there in ^^ of a rod ?
8. What 7 equal numbers when added give 42?
What part of 42 is the sum of 4 of these numbers ?
9. If 15 men dig a ditch in 8 days, how long will
it take 6 men to dig the ditch ?
10. If blueberries are 8 cents a quart, what part
of a peck can be bought for 56 cents ?
11. Which is the largest and which the smallest
of the fractions ^, J, and f?
12. If a butcher leaves home in the morning with
100 lb. of beef and returns at night with 12^ lb.,
wliat part of his beef has he sold ?
13. If a ton of hard coal occupies 32 cu. ft. of
space, how many cubic feet are there in IJ tons?
14. If 7 lb. of pork are sold for $1, how many
cents must be paid for 1 lb. ?
15. If a quart and a pint are taken from a gallon
of vinegar, what part of the gallon remains ?
120 MENTAL ABITHMETIG.
LoBSon 51.
1. A sold 4f acres of land to B, and 9^ acres to C.
How many acres did A sell ?
2. If ^ff of a ton of coal costs $3.50, what is the
cost of 8 tons ?
3. From what number must 4f be subtracted to
leave a remainder of 9^ ?
4. If John walks 9§ miles in 3J hours, how many
miles does he walk in 1 hour ?
5. If a man earns $8f in 5 days, how much does
he earn in 2 days ?
6. How long will it take a boy to earn $7 if he
earns 87|- cents a day ?
7. The product of two numbers is 17^. If one
number is 3^ what is the other ?
8. By what number must 7| be divided to give 1^
as a quotient ?
9. How much greater is J of 40 than ^ of 40 ?
10. If ^ of a number is 5 greater than i of the
number, what is the number ?
11. Mr. Smith sold a cow for $36, which was i
more than the cost. What was the cost of the cow ?
* 12. What number increased by J of itself is equal
to 24? 42? 48? 64? 96?
13. Thomas has 5 times as many cents as Philip.
If together they have 42 cents, how many has each ?
14. George has f as many marbles as Henry and
together they have 40 marbles. How many has
each?
15. The sum of 2 numbers is 48 and the smaller
is I of the larger. What are the numbers ?
MENTAL ABITHMETIC. 121
Iiesflon 52.
1. At $5J a ton what part of a ton of coal can be
bought for $1^ ? $3|^ ? $3 ?
2. Frank caught 3 bass, one of which weighed
2 lb. 14 oz., the second 1 lb. 4 oz., and the third 3 lb.
10 oz. What was the weight of the three fish ?
3. What 9 equal numbers added together make
30 ? What part of 30 is the sum of 5 of these num-
bers ? 3 of these numbers ?
4. What is the distance around a room 16^ ft.
long and lOf ft. wide ?
5. If the sum of the length and width of a room
is 30 ft. and the width is § of its length, what are
the dimensions of the room ?
6. At 37|^ cents a yard how many yards of cloth
can be bought for $2 ? for $5 ? for $7 ?
7. A man invests J of his capital in bank stock, i
in railroads, i in real estate, and has $1000 left.
What is the amount of his capital ?
8. How many times can a measure holding J of a
pint be filled from a keg containing 2^ gal. ?
9. A man bought a pair of gloves for $1|-, a neck-
tie for $^, and 2 collars at $i apiece. What change
should he receive from $5 ?
10. One-half of a cord of wood at $6 a cord will
pay for what part of a ton of coal at $5^ a ton ?
11. Mr. Peters sold ij- of his farm, then J of the
remainder. What part of the farm did he keep ?
12. If a man's expenses average 62^ cents for
every dollar that he earns, what part of his income
does he spend ? What part does he save ?
122 MENTAL ABITHMETIC.
LeBSon 53.
1. If 3 qt. of cream can be bought for <|^1, what is
the cost of 1^ pt. ?
2. A bushel contains IJ cubic feet. How many
cubic feet are there in 6 bushels ? *
3. If f of a peck of cranberries costs 27 cents, what
is the cost of ^ of a bushel ?
4. If A can build a fence in 3^ days and B in 4^
days, what part of the fence can each build in 1 day ?
5. If B can walk 4}- miles an hour and C can ride
15 miles an hour on a bicycle, what part of an hour
must C ride to go as far as B can walk in 1 hour ?
6. What is the cost of 6^ cords of pine wood at
$3 a cord ? of 7 cords at $3^ a cord ?
7. How many five-cent pieces make $^jf ?
8. If a sailboat sails 7^ miles in 2^ hours, what is
the rate per hour ?
9. How many cubic feet are there in a piece of
timber 12 ft. long, 1^ ft. wide, and f ft. thick ?
10. Assuming that 7-)- gal. make a cubic foot of
water, what part of a cubic foot of water is 1 gal. ?
11. How many gallons are there in f of a cubic foot ?
12. If a cubic foot of water weighs 62^ lb., what
is the weight of 2 cu. ft. ? of ^ cu. ft. ?
13. Joseph and Thomas start from the same place
on bicycles. Joseph rides south at the rate of 9f
miles per hour. Thomas rides north llj miles per
hour. How far apart are they at the end of 1 hour ?
14. If a merchant loses ^ of his capital 1 year and
J of the remainder the next year, what part of his
capital does he lose in the two years ?
MENTAL ARITHMETIC. 123
LeBson 54.
1. The sum of 8 equal numbers is 3^ ? What part
of 3f is the sum of 7 of these numbers ?
2. If a passenger train runs from Boston to Port-
land in 3f hours, how many hours will it take a
freight train running f as fast?
3. If a freight train at f the rate of an express
train runs 48 miles in 2 hours, how long ^ill it take
the express train to run the same distance ? .
4. Two boys ar,e 27 miles apart and walk toward
each other, one at the rate of 3^ miles per hour, the
other at 3^ miles per hour. What part of the dis-
tance will remain at the end of 2 hours ?
6. If plums can be bought at the rate of 5 for 3
cents, what patt of a dollar would 25 plums cost ?
6. If 20 pounds of sugar can be bought for $1,
what part of a ton can be bought for $5 ?
7. If a knife costing $1 is sold for $1.30, the
profit is what part of the cost ?
8. If the upper surface of a paving block is -j^ of
a square foot, how many blocks will be needed to
pave 8| sq. ft. ?
9. If 16 is 2i times a number, what part of 16 is
the number ?
10. If ^ of a stick f of a yard long is cut off, what
part of a yard is left ?
11. If grapes cost 37^ cents a basket, what frac-
tion of a dollar will be left after the cost of 2 baskets
is taken from it ?
12. How many baskets of grapes at $f a basket
can be bought for $12 ?
124 MENTAL ARITHMETIC.
LeBBon 55.
1. A bankrupt paid 62^ cents on a dollar. What
part of his claim did each creditor receive ?
2. A milkman sold the same amount of milk to
each of 8 families and sold 5 gal. in all. How many
quarts did each family buy ?
3. If a man agrees to work 10 hours a day, what
part of a day's wages should he receive for working
3 hours and 45 minutes ?
4. A and B hired a pasture. A put in 8 cows, B
13 cows. What part of the rent should each pay ?
5. A and B are partners. A owns $3000 of the
capital and B $8000. What part of the profits
should B receive ?
6. A and B divide profits in proportion to their
capital. If A receives $500 and B $200, what part
of the capital belongs to A ?
7. Thomas earns $2^ a day and George $1^.
They work the same number of days and earn to-
gether $40. What part of it belongs to George ?
8. If f of a piece of work can be done in a day, in
how many days can the work be done ?
9. If A can mow ^ of a field in ^ of a day, in how
many days can he mow the field ?
10. A man divided $48 between his 2 sons so that
one received i as much as the other. What part of
$48 did each receive ? How many dollars ?
11. John has f of a melon. To how many boys
can he give ^ of a melon ? J of a melon ?
12. If 4 cents are paid for the use of a dollar for
a year, what part of a dollar is paid ?
M£NTAL ARITHMETIC. 125
Lesson 56.
1. A is 12^ miles behind B. In how many hours
will he overtake B, if he walks IJ miles an hour
faster than B ?
2. A freight train runs 18 f miles an hour, and an
express train runs 35f miles. How many miles does
the express gain on the freight in an hour ?
3. What part of a bushel of chestnuts would be
needed to give 24 boys a pint apiece ?
4. If a post 5i ft. high casts a shadow 2 ft. long,
what part of the height of the post is the length of
its shadow ?
5. How high is a pole that casts a shadow 6 times
as long as the shadow of the post in the last ex-
ample? 8 times as long?
6. If a man walks at the rate of ^f miles an hour,
how far will he walk in 7 hours ?
7. If A can build a wall in 2^ days, what part can
he build in 1 day ? in 2 days ?
8. If A can mow a field in 2^ days and B can mow
it in 2^ days, what part can each mow in 1 day?
What part can both together mow in 1 day ?
9. What will remain of $5 after paying for beef
$lf, for .sugar $1 J, and for apples $1^ ?
10. If Mr. Brown sold a horse, losing ^ of the
cost, for what part of the cost did he sell the horse ?
What did the horse cost if he was sold for $70 ?
11. By investing $80 B gains $4 a year. C in-
vests $70 and gains $3 a year. The annual income
of each man is what part of his investment ? Which
makes the better investment ?
CHAPTEE IV.
PERC3BNTAGE.
Lesson 1.
Per cent means hundredths. 10% (10 per cent) of anything
is 10 hundredths of it.
1. What part of a circle is 50% of it ?
2. How many quarts in 50% of 1 gal. ?
3. If a boy ha? 40 cents, how much will he have
after spending 50% of his money?
4. 50% of 34 is what number?
.5. After selling 50% of his cows a dealer had 15
cows left. How many had he at first ?
6. What part of a circle is 25<fo of i* ?
7. What part of an apple is 25% of it?
8. How many quarts in 25% of 1 bu. ?
9. A farmer sold 25% of his flock of sheep.
What part of his flock did he keep ?
10. 25% of a mixture is water, and the mixture
contains 10 lb. of water. What is the weight of the
mixture ?
11. A frost killed J of the plants in a garden.
What per cent of the plants did the frost kill?
What per cent remained alive ?
MENTAL ABITHMETIG.
127
LoMon 2.
1. What part of a circle is 33^% of it ?
2. How many minutes in 33^% of 1 hour ?
3. How many doUars in 33^% of $36 ?
4. If a man gave away ^ of his property, what per
cent of his property did he give away ?
5. In an orchard of 42 trees 33^^^ are pear trees.
How many pear trees are there in the orchard ?
6. What per cent of a circle is f of the circle ?
7. A boy having 21 peaches gave away 66f % of
them. How many peaches did he give away ?
8. How many inches in 66f % of a yard ?
9. If a boy lost i of his marbles, what per cent of
his marbles did he have left?
10. After selling 33^ per cent of his flock of
sheep, a farmer had 32 sheep left. How many had
he at first ?
11. What part of a circle is 16f % of it ?
12. If a pie is divided equally among 6 boys, what
per cent of the pie will each boy have ?
13. How many eggs in 16f ^ of a dozen of eggs ?
14. Fifty dollars is 16§% of what?
15. A owns 33^^ of a vessel and B 16§ per cent.
A's share is how many times B's share ?
16. Eleven is 16 J ^ of what number ?
128
MENTAL ARITHMETIC.
Lesson 3.
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1. What part of a rectangle is 20% of it ?
2. Twenty is what part of 100 ?
3. If a rectangle contains 40 sq. ft., how many
square feet are there in 20% of it? in 40% of it?
in 60% of it ? in 80% of it? in 100% of it?
4. If a piece of cloth 10 ft. long shrinks 20%,
how long will the cloth be after shrinking ?
6. Peter's age is 20% of his father's. If Peter is
9 years old, how old is his father ?
6. A farmer sold 20% of his land to A, 25% to B,
and 50% to C. What per cent had he left?
7. Wtat part of a rectangle is 10% of it ?
8. How many square rods in 10% of an acre ?
9. How many pounds in 10% of a ton?
10. What part of 20 is 2 ? What per cent ?
11. What per cent of 20 is ^^ of 20 ? ^ of 20 ?
^^ of 20 ?
12. Philip gave 10% of a melon to each of 4 boys.
What per cent of the melon remained ?
13. A owns 25% of a factory and B 10%. A's
share is how many times B's share ?
14. What per cent of a farm would remain after
^ of it was sold ?
MEITTAL ABITHMETIG.
129
LoMon 4.
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1. What per cent of $12 would each boy have, if
the money was divided equally among 3 boys ? 2
boys ? 4 boys ? 10 boys ? 6 boys ? 6 boys ?
2. How many seconds in 25% of 1 minute ? 50% ?
16f % ? 20% ? 33i% ? 66f % ? 100% ? 10% ?
3. What per cent of a ship does a man own, if he
ownsiofit? f? i? J? T?^? i? I?
4. What per cent of a farm remains after there is
sold I of it? i? i? i? i? A^
5. A man divided his property equlEilly among his
children. How many children had he if each
received 25% of it? 50% ? 16f % ? 33^% ? 20% ?
6. 16f % of an orchard of 48 trees are peach trees,
25% are pear trees, and the rest are apple trees.
How many are there of each kind ?
7. What is the number of which 12 i^ 50% ?
25%? 75%? 66|%? 40%? 60%? 10%? 16f % ?
8. A owns 50% of a railroad. What part of his
share does he sell if he sells 25% of the railroad?
10% ? 20% ? 16§% ? 33i% ? 40% ?
9. What per cent of 10 is 1 ? 1§? 2^? 4? '5?
3i? 6f? 7^? 9? 10?
130
MENTAL ABITHMETIG.
Lesson 5.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
$1 is what part of f 100 ?
$2 is what part of $100 ?
$S is what part of $100 ?
$1 is what part of $50 ?
$2 is what part of $50 ?
$3 is what part of $50 ?
$1 is what part of $25 ?
$2 is what part of $25 ?
$3 is what part of 926 ?
$1 is what part of $10 ?
$2 is what part of $10 ?
$3 is what part of $10 ?
$5 is what part of $100 ?
$5 is what part of $50 ?
$5 is what part of $25 ?
$5 is what part of $10 ?
is what part of $100 ?
is what part of $50 ?
is what part of $25 ?
$8 is what part of $10 ?
$12 is what part of $100 ?
$12 is what part of $50 ?
$12 is what part of $25 ?
$20 is what part of $100 ?
$20 is what part of $50 ?
$20 is what part of $25 ?
$30 is what part of $100 ?
$30 is what part of $50 ?
$40 is what part of $100 ?
$40 i9 what part of $50 ?
$1 is what % of $100 ?
$2 is what % of $100 ?
$3 is what % of $100 ?
$1 is what % of $50 ?
$2 is what % of $50 ?
$3 is what % of $50 ?
$1 is what % of 925 ?
$2 is what % of $25 ?
$3 is what % of $25 ?
$1 is what % of $10?
$2 is what % of $10 ?
$3 is what % of $10 ?
$5 is what % of $100 ?
$5 is what % of $50 ?
$5 is what % of $25 ?
$5 is what % of $10 ?
is what % of $100 ?
is what % of $50 ?
$8 is what % of $25 ?
$8 is what % of $10 ?
$12 is what % of $100 ?
$12 is what % of $50 ?
$12 is what % of $25 ?
$20 is what % of $100 ?
$20 is what % of $50 ?
$20 is what % of $25 ?
$30 is what % of $100 ?
$30 is what % of $60 ?
$40 is what % of $100 ?
$40 is what ^ of $50 'f
MENTAL ARITHMETIC. 131
Lesson 6.
1. $6 is what part of $100 ? $6 is what % of $100 ?
2. $6 is what part of $50 ? $6 is what % of $50 ?
3. $6 is what part of $25 ? $6 is what % of $25 ?
4. $6 is what part of $10 ? $6 is what % of $10 V
5. $10 is what part of $100 ? $10 is what % of $100 ?
6. $10 is what part of $50 ? $10 is what % of $50 ?
7. $10 is what part of $25 ? $10 is what % of $25 ?
8. $15 is what part of $100 ? $15 is what % of $100 ?
9. $15 is what part of $50 ? $15 is what % of $50 ?
10. $15 is what part of $25 ? $15 is what % of $25 ?
11. $16 is what part of $100 ? $16 is what % of $100 ?
12. $16 is what part of $50 ? $16 is what % of $50 ?
13. $16 is what part of $25 ? $16 is what % of $25 ?
14. $24 is what part of $100 ? $24 is what % of $100 ?
15. $24 is what part of $50 ? $24 is what % of $50 ?
16. $24 is what part of $25 ? $24 is what % of $25 ?
17. $7 is what part of $100 ? $7 is what % of $100 ?
18. $7 is what part of $50 ? $7 is what % of $50 ?
19. $7 is what part of $25 ? $7 is what % of $25 ?
20. $7 is what part of $10 ? $7 is what % of $10 ?
21. $9 is what part of $100 ? $9 is what % of $100 ?
22. $9 is what part of $50 ? $9 is what % of $50 ?
23. $9 is what part of $25 ? $9 is what % of $25 ?
24. $9 is what part of $10 ? $9 is what % of $10 ?
25. $11 is what part of $100 ? $11 is what % of $100 ?
26. $11 is what part of $50 ? $11 is what % of $50 ?
27. $11 is what part of $25 ? $11 is what % of $25 ?
28. $35 is what part of $100 ? $35 is what % of $100 ?
29. $35 is what part of $50 ? $35 is what % of $50 ?
30. $45 is what part of $100 ? $45 is what % of $100 ?
132 MENTAL ARITHMETIC.
LeBBon 7.
1. 12 bushels are what part of 100 bushels ? 12
bushels are what % of 100 bushels ?
2. 12 quarts are what part of 50 quarts ? 12 quarts
are what % of 50 quarts ?
3. 12 pints are what part of 25 pints ? 12 pints
are what % of 25 pints ?
4. 6 grains are what part of 100 grains? 6 grains
are what % of 100 grains ?
5. 6 ounces are what part of 50 ounces ? 6 ounces
are what % of 50 ounces ?
6. 6 pounds are what part of 25 pounds ? 6 pounds
are what % of 25 pounds ?
7. 7 dozen are what part of 100 dozen ? 7 dozen
are what % of 100 dozen ?
8. 7 gross are what part of 50 gross ? 7 gross are
what % of 50 gross ?
9. 7 reams are what part of 25 reams ? 7 reams
are what % of 25 reams ?
10. 10 feet are what part of 100 feet ? 10 feet are
what % of 100 feet?
11. 10 inches are what part of 50 inches? 10
inches are what % of 50 inches ?
12. 10 lines are what part of 25 lines ? 10 lines
are what % of 25 lines ?
13. 5 tons are what part of 100 tons ? 5 tons are
what % of 100 tons ?
14. 5 cords are what part of fifty cords ? 5 cords
are what % of 50 cords ?
15. 5 acres are what part of 25 acres ? 5 acres
are what % of 25 acres ?
MJENTAL ABITHMBTIC. 133
LeMon 8.
1. $& is what part of $75 ? $5 is what % of 975 ?
2. 95 is what part of $55 ? $5 is what % of 955 ?
3. $5 is what part of $35 ? 95 is what % of $35 ?
4. 95 is what part of $15 ? $5 is what % of $15 ?
5. 3 is what part of 100 ? $3 is what % of $100 ?
6. 11 is what part of 100 ? $11 is what % of $100 ?
7. 12 is what part of 100 ? $12 is what % of $100 ?
a 15 is what part of 100 ? $15 is what % of $100 ?
9. 27 is what part of 100 ? $27 is what % of $100 ?
10. 33 is what part of 100 ? $33 is what % of $100 ?
11. 3 is what part of 4 ? $3 is what % of $4 ?
12. 5 is what part of 10 ? $5 is what % of $10 ?
13. 2 is what part of 8 ? $2 is what % of $8 ?
14. A man having $100 spent $10; what % of his
money did he spend ? What part of 100 is 10 ?
15. A boy who had 10 cents gave away 3 cents; what
^ of his money did he give away ?
16. A little girl had 5 coppers ; she lost one and gave
away two; what % of the money did she have left ?
17. In an orchard of 100 trees there are 11 pear trees ;
what % of the orchard are pear trees ?
18. On a ship the officers and men number 25 and
the passengers 5 ; what ^ of the persons on the ship are
passengers ?
19. 18 students tried an examination and 9 failed to
pass ; what ^ of those who tried failed ?
20. 3 dozen eggs were sent to market, but 1 dozen
was broken on the way ; what % was broken ?
21. A man has $40. If he spends 60^ of his money,
what per cent will he have left ?
134 MENTAL ABITHMETie.
Lesson 9.
1. A man with $100 spent $17 for provisions and
$S for a coat ; what per cent of his money did he
spend ?
2. James paid 5 cents for a top and 1 cent for a
top-string, and had 4 cents left ; what per cent of his
money did he spend ?
3. Sarah had 5 oranges and gave away 2 of them ;
what per cent did she give away ?
4. In a certain school there were 16 boys and 34
girls ; what per cent of the total number of scholars
were boys ? what per cent were girls ?
5. A furnace burns 8 tons of coal while a large
stove bums 2 tons ; what per cent of the coal burned
by both is consumed by the stove ? what per cent
by the furnace ?
6. In a certain factory there are employed 20 men,
60 women, 12 boys, and 8 girls; what per cent of
the employed are men ? women ? boys ? girls ?
7. On a steamship there are 150 First Cabin pas-
sengers, 150 Second Cabin, and 200 Steerage ; what
per cent of all the passengers are Steerage ?
8. In a certain school there are 10 teachers ; 5
teach languages, 2 teach mathematics, and 3 teach
history ; what per cent teach languages ? what per
cent mathematics ? what per cent history ?
9. Julia can do f of her sewing in 1 day ; what
% of her sewing can she do in 1 day ?
10. $3^ is what % of $100 ?
11. $3Si is what ^ of $50 ? $66| is what % of
$100 ? $66f is what % of $200 ?
MEKTAL ARITHMETIC. 135
Lesson 10.
1. How many bushels are 50^ of 100 bushels ?
2. How many sheep are 40^ of 120 sheep ?
3. How many pounds are 30^ of 150 pounds ?
4. How many apples are 3^ of 300 apples ?
5. How many cords are 50^ of 50 cords ?
6. How many chairs are 40^ of 40 chairs ?
7. How many horses are 30^ of 50 horses?
8. How many pecks are 3^ of 150 pecks ?
9. How many rods are 60% of 80 rods?
10. How many feet are 10% of 250 feet ?
11. How many yards are 6% of 500 yards ?
12. How many barrels are 10% of 30 barrels?
13. A man had 50% of his money invested in real
estate, 2o^o invested in bonds, and the remainder,
4^5000) in a bank ; how many dollars had he ?
14. 5000 is 25% of what number?
15. A man bought a horse for $100 and sold him
again for $125 ; how many dollars did he gain ?
what per cent of the cost did he gain ?
16. A man bought a cow for $50 and sold her again
for $40; how many dollars did he lose ? what per
cent of the cost did he lose ?
17. A man bought a horse for $200 and sold him
again for $240, after keeping him for 5 jeeeks at a
cost of $4 per week ; what per cent of the cost did
the man gain ?
18. A man bought a house for $2500 and sold it
for $3000 ; what per cent of the cost did he gain ?
19. A man bought a house for $2500 and sold it
for $2000 ; what per cent of the cost did he lose ?
136 MENTAL ABITHMBTIO.
Ziasaon 11.
1. A shop-keeper had 75 yards of silk and sold 25
yards ; what per cent of his silk did he sell ?
2. Two men hired a pasture for $100 ; one put in
7 horses, and the other 3 horses ; what per cent of the
$100 ought each to pay ?
3. Two inen bought a house for $2500 ; one paid
$1500, the other $1000 ; what per cent of the house
does each own ?
4. A rod of iron, when heate^, increased in length
by 1 inch ; if the length of the rod, before heating,
was 100 inches, by what per cent of its original length
has it increased in length ?
5. A piece of iron weighs 7 ounces in air, but
when weighed in water, its weight is only 6 ounces ;
what per cent of its weight in air has the piece of
iron lost by being weighed in water?
6. Out of an army of 10,000 men, 3000 were killed
in a battle ; what per cent of the men were killed ?
7. A small bank had $50,000 in deposits ; $10,000
were deposited by persons living out of town ; what
per cent of the deposits belonged to persons living in
town ?
8. To pay the annual expenses of a certain school,
$30,000 aie required, while to pay those of another
school only $20,000 are necessary ; what per cent of
the larger sum is the difference? what per cent of
the smaller sum is the difference ?
9. A man worked 4 days out of 6 ; what was the
per cent of time that he was idle ?
10. What per cent of 5 is 3 ? of 3 is 2 ?
MENTAL ABITHMBTIG. 137
L a aao n 12.
1. A merohant bought 30 barrels of flour for
$100, and sold the flour at $4.50 per barrel. How
many dollars did he gain ? How much per cent ?
2. Borrowed $2000 at 5^, and with this sum
bought goods which were sold at the end of a year
for $2300. If $100 was paid for insurance, storage,
etc., what per cent on the first cost was gained ?
3. James bought 5 doz. oranges for $2. A dozen
and a h^lf spoiled, but he sold the remainder for 4
cents apiece ; what per cent of the cost did he lose ?
4. George bought 3 doz. oranges for 75 cents and
sold them at 3 cents apiece ; how many cents did he
gain ? What per cent of the cost did he gain ?
5. Bought shoes at $3 per pair and sold them at
$3.75 ; what per cent waB gained ?
6. Bought hats at $2 each and sold them at $1.75;
how many cents were lost on each hat ? Wl\^t per
cent of the cost was lost ?
7. A man bought a horse for $100 and sold him
for $112*; what per cent of the cost did he gain?
8. A man bought a horse for $200 and sold him
at a price by which he lost 10% of the cost; at what
price did the man sell the horse ?
9. A grocer sold flour, for which he paid $3.50 per
barrel, at an advance of 20% ; at what price per bar-
rel did he sell the flour ?
10. A young man bought a watch for $20 and sold
it so as to gain 5% ; at what price did he sell it?
11. A man bought a wagon for $100 and sold it
for $90; what per cent of the cost did he lose ?
138 MENTAL ABITHMBTIG.
ZaeMon 13.
1. A lawyer, as agent, borrows $2000, what is his
commission at 2^ ?
2. A commission merchant sells wheat to the
amount of $3t)00 ; what is his commission at 2^ ?
3. A broker sells stock for $5000; what is his
commission at ^ of 1^ ?
4. What is the commission on $300, at 2|^ ?
5. If I allow a man 5% for collecting sums of
money due me, how many dollars must I pay him
for collecting $250 ?
6. A gentleman sold 10 shares in the Home In-
surance Company at 6^ advance, the par value of a
share being $100 ; how many dollars did he receive ?
7. Bought 8 shares of a certain railroad at 2^ dis-
count, the par value of the stock being $100 ; how
many dollars did the stock cost ?
8. A farmer sent to a commission merchant farm
produce, which the merchant sold for $75, and
charged a commission of 3^ ; how many dollars did
the farmer receive ?
9. A man borrowed $600 through a broker who
asked 2^ commission ; how many dollars did the
borrower pay the broker for commission ?
10. If a man allows his agent 3^ for disbursing
$1500, on his account, how many dollars does the
agenf s commission amount to ?
11. A merchant sent $10,000 to his agent in
Havana for the purchase of sugar; if the agent's
commission is 1^ of the sum sent, how many dol-
lars does he invest in sugar ?
MENTAL ARITHMETIC. 139
LesBon 14.
1. What is the cost of insuring a vessel in the sum
of ^f 10,000 at 3%?
2. The rate of insurance for vessels coasting in
Long Island Sound is 4^ per annum; what is the
annual premium for insuring a schooner for 95000 ?
Note. Money paid for insurance is called the premium of
insurance.
3. A house, worth $2500, is insured for } of; its
value at f of 1%^ what is the premium?
4. Mr. Smith buys a house for $12,000, and gets
it insured for f of its value at ^ of 1^ ; this house is
burned ; what is Mr. Smith's loss ? What is the loss
of the Insurance Company ?
5. What is the premium, at 2^, for insuring a
steamship cargo from New York to Liverpool, if the
cargo, worth $100,000, is insured for f of its value?
€. A business man insures his office furniture for
$300 at 14^% ; what is the premium ?
7. The machinery of a factory, worth $10,000, is
insured for ^ its value at 3^; what is the premium?
8. A man insures his goods for $600 at 2^^;
what premium does he pay ?
9. A man insured his dwelling house for $2500
at 1^^ ; what premium does he pay ?
10. A writer insures his books for $800 at f of
1 ^ ; what is the premium ?
11. A merchant insures his stock, worth $25,000^
for } of its value ; what is the premium at 2^?
12. What is the premium, at | of 1^, for insurance
of $500 on household furniture ?
140 MBKTAL ABITHXSTIC.
LeMKm 19.
1. At the rate of 6% per annum, what is the in-
terest for one year on $100? $200? $300? $400?
2. At the rate of 6^ per annum, what is the in-
terest for one year on $400 ? $500 ? $600 ? $700 ?
3. At the rate of 4^ per annum, what is the in-
terest for one year on $100 ? $200 ? $300? $400 ?
4. At the rate of 3^ per annum, what is the in-
terest for one year on $400 ? $500? $600? $700?
5. At the rate of 6^ per annum, what is the in-
terest for two years on $100 ? $200*? $300? $400?
6. At the rate of 5^ per annum, what is the in-
terest for two years on $300 ? $400? $500? $600?
7. At the rate of 4^ per annum, what is the in-
terest for two years on $100 ? $200? $300? $400?
8. At the rate of 3% per annum, what is the in^
terest for two years on $300 ? $400 ? $500 ? $600 ?
9. At the rate of 6% per annum, what is the in-
terest for three years on $100? $200? $300? $400?
10. At the rate of 6% per annum, what is the in-
terest for three years on $100 ? $200 ? $300 ? $400 ?
11. At the rate of 4% per annum, what is the in-
terest for three years on $800 ? $400 ? $500 ? $600 ?
12. At the rate of 3^ per annum, what is the in-
terest for three years on $100? $200? $300? $400?
13. At the rate of 6% per annum, what is the in-
terest for one year on $50 ? $60? $80? $90? $120?
14. At the rate of 5^ per annum, what is the in-
terest for one year on $50 ? $60 ? $80 ? $90 ? $120 ?
15. At the rate of 4^ per annum, what is the in-
terest for one year on $80 ? $90? $120? $160? $180?
MENTAL ARITHMETIC. 141
Lesson 16.
1. At what rate per cent must $100 be put on in-
terest to gain $6 in one year ?
2. At what rate per cent must $50 be put on in-
terest to gain $3 in one year ?
3. At what rate per cent must $25 be put on in-
terest to gain $1.50 in one year ?
4. At what rate per cent must $100 be put on in-
terest to gain $5 in one year ?
5. At what rate per cent must $50 be put on in-
terest to gain $2.50 in one year ?
6. At what rate per cent must $25 be put on in-
terest to gain $1.25 in one year ?
7. At what rate per cent must $100 be put on in-
terest to gain $4 in one year ?
8. At what rate per cent must $50 be put on in-
terest to gain $2 in one year ?
9. At what rate per cent must $25 be put on in-
terest to gain $1 in one year ?
10. At what rate per cent mustv$100 be put on
interest to gain $3 in one year ?
11. At what rate per cent must $50 be put on in-
terest to gain $1.50 in one year ?
12. At what rate per cent must $25 be put on in-
terest to gain $0.75 in one year ?
13. At what rate per cent nm84^ $100 be put on
interest to gain $10 in two years ?
14. At what rate per cent must $200 be put on
interest to gain $16 in two years ?
15. At what rate per cent must $60 be put on in-
terest to gain $3 in two years ?
142 MENTAL ASITHMETIC.
laesflon 17.
1. For what time must $100 be on interest at 6^
a year to gain $36 ?
2. For what time must $50 be on interest at 5^
a year to gain $5 ?
3. For what time must $200 be on interest at 4%
a year to gain $24 ?
4. For what time must $300 be on interest at 6%
a year to gain $48 ?
5. For what time must $10,000 be on interest at
3% a year to gain $90 ?
6. For what time must $500 be on interest at 4^
a year to gain $40 ?
7. For what time must $350 be on interest at 5^
a year to gain $35 ?
8. For what time must $16 be on interest at C%
a year to gain $1.92 ?
9. For what time must $45 be on interest at 4^
a year to gain $1.80 ?
10. For what time must $24 be on interest at 5^
a year to gain $3.60 ?
11. For what time must $8 be on interest at 7^
a year to gain $1.12 ?
12. For what time must $80 be on interest at 3^
a year to gain $7.20 ?
13. For what time must $33 be on interest at 8^
a year to gain $2.64 ?
14. For what time must $150 be on interest at
4% a year to gain $24?
15. For what time must $900 be on interest at
5% a year to gain $90 ?
MENTAL ARITHMETIC. 143
Lesson 18.
1. What principal, at 6%, will gain $6 in one year ?
2. What principal, at 5^, will gain $5 in one year ?
3. What principal, at 4%, will gain $4 in one year ?
4. What principal, at 3%, will gain $3 in one year ?
5. What principal, at 6%; will gain $12 in one year ?
6. What principal, at 5%, will gain $15 in one year?
7. What principal, at 3%, will gain $12 in one year?
8. What principal, at 4%, will gain $40 in one year ?
9. What principal, at 5%, will gain $10 in 2 years ?
10. What principal, at 4%, will gain $60 in 3 years ?
11. What principal, at 6%, will gain $120 in 2 years ?
12. What principal, at 8%, will gain $24 in 2 years ?
13. What principal, at 4%, will gain $24 in 2 years ?
14. What principal, at 3%, will gain $18 in 3 years ?
15. What principal, at 7%, will gain $14 in 4 years ?
16. What principal, at 6%, will gain $27 in 3 years ?
17. What principal, at 5%, will gain $100 in 2 years ?
18. What principal, at 4%, will gain $80 in 5 years?-
19. What principal, at 8%, will gain $8 in 2 years?
20. What principal, at 4 % , will gain $1.60 in 2 years ?
21. What principal, at 10%, will gain $50 in 5 years ?
22. What principal, at 2%, will gain $18 in 2 years ?
23. What principal, at 5%, will gain $30 in 6 years ?
24. What principal, at 6%, will gain $48 in 2 years ?
25. What principal, at 3%, will gain $18 in 3 years ?
26. What principal, at 4%, will gain $400 in 2 years ?
27. What principal, at 6%, will gain $300 in 2 years ?
28. What principal, at 6%. will gain $3 in 2 years ?
29. What principal, at 4%, will gain $2 in 2 years ?
30. What principal, at 4%, will gain $200 in 2 years ?
144 MENTAL ARITHMETIC.
LeBBon 19.
1. What is the annual income from an investment
of $200 at the rate of 5% a year?
2. At the rate of 4% a year, what is the annual
interest return from an investment of $1200 ?
3. In a savings bank a man has a deposit of $350 ;
at the rate of 4% what will the man receive for in-
terest at the end of the year?
4. What is the interest on $42 for one year at
4%? at5%? at6%?
5. A man, having $30,000 invested at the rate of
5%, saved 33^% of the income; how many dollars
did he save per year ?
6. A man hires $1000 at 5%, and loans the money
at 6% ; how many dollars does he gain per year ?
7. A man loaned $50 at 6%, $300 at 5%, and
$100 at 4%; how many dollars a year does he re-
ceive from these loans ?
8. A business man borrowed $1200 at 6% and in-
vested the money in such a way as to yield him 15% ;
how many dollars did he gain in a year ?
9. What is the interest at the rate of 5% per
annum on $100 for six months ?
10. What is the interest at the rate of 4% per an-
num on $50 for one year and six months ?
11. What is the interest at the rate of 3% per
annum on $200 for three years and four months ?
12. What is the interest at the rate of 6% per
annum on $25 for two years and six months ?
13. What is the interest at the rate of 5 % per
annum on $500 for four months ?
CHAPTER V.
MISCELLANEOUS PROBLEMS.
Lesson 1.
1. A man bought a sleigh for $20, and gave $9 to
have it repaired and painted; then he sold it for
$35 ; how many dollars did he gain ?
2. By going on an errand James earned 10 cents ;
with the money he bought apples at 3 for 2 cents ;
how many apples did he buy ?
3. A man bought a hat for $3, a pair of shoes for
$5, and a pair of gloves for $2. He handed the
salesman a twenty-dollar bill; how many dollars
should the salesman give back ?
4. How many oranges can be bought for 26 cents,
when they are selling at the rate of 2 for 5 cents ?
5. Which is the greater, ^or|? i or ^? ^or^?
iOT^\? ior^-V?
6. 2 is J of what number ? ^ of what ? | of what ?
y\y of what ? j^y of what ? y^ ^^ what ?
7. George and Harry went nutting. George gath-
ered ^ and Harry ^ of a bushel of hickory nuts;
how many more twenty-fourths of a bushel did George
gather than Henry ?
8. George's uncle gave him $125. George spent
^ of this sum for a bicycle ; how many dollars did
he have left ?
9. Which is the greater, f of 42 or | of 42 ? f
of 35 or I of 35 ?
146 MENTAL ARITHMETIC.
Le88on 2.
1. A flour merchant gave at Christmas 10^ bar-
rels of flour to his men^ giving i barrel to each man ;
how many men were there ?
2. In 12f how many thirds ? In 16| how many
sixths? In 20^ how many eighths? In 25% how
many fifths ?
3. At Christmas EoUo's uncle George gave him $2
to spend in any way he liked ; EoUo bought a copy
of Robinson Crusoe for $1, and spent J of the money
that remained for candy; after buying the candy,
how much money did RoUo have ?
4. At i dollar per yard how many yards of cloth
can be bought for $8^ ?
5. Under the boiler of a steam engine are burned
each day 2J tons of coal; how many tons will be
burned in 7 days ?
6. Find i of 100, i of 100, i of 100, f of 100, ^ of
100, i of 100, ^ of 100, ^ of 100.
7. Three tons of coal are distributed equally among
12 poor families ; what part of a ton does each family
receive ?
8. If a man receives $5 for 4 days' work, how
much does he receive per day?
9. Three men paid in equal shares $126 for a
horse, and paid $3 a week for keeping him ; at the
end of 5 weeks they sold him for $130 ; how much
did each man lose by the transaction ?
10. A merchant bought a piece of cloth for $24,
and sold it for J of what he gave for it ; how many
dollars did he sell it for ?
MENTAL ARITHMETIC. 147
Lesaon 3.
1. A young lady bought a hat for $6, a veil for i
dollar, and 2 hat pins for ^ dollar. She handed the
saleswoman a ten-dollar bill ; how much money did
the young lady receive in change ?
2. Stephen's father gave him the use of a piece
of ground. Stephen planted J with potatoes, J with
parsnips, and ^ with celery. How many twenty-
sevenths were left to plant with corn ?
3. A merchant bought ^ of a ship, and some
time afterwards bought ^ of the same ship; how
many sixty-fourths of the ship did he own ?
4. If 4 tons of coal cost f 26, what will be the
cost of 10 tons ?
5. James is twice as old as John, and the sum of
their ages is 9 years ; what is John's age ?
6. A certain sum of money will support a family
of 6 persons for 12 weeks ; how many persons will
it support for 18 weeks ?
7. George had $1 : he spent J of it for fish-hooks
and a line, and the remainder for a bait-box ; how
many cents did he pay for the bait-box ?
8. At Christmas a poor woman received from one
person f of a ton of coal, from another |, and from
a third J; how much did she receive in all ?
9. If a horse eats ^ of a bushel of oats in 1 day,
how many days will it take him to eat 1 bushel ?
10. If oats cost } of a dollar a bushel, what will
6 bushels cost ?
11. A boy gave 4 other boys f of an orange apiece ;
how many oranges did it take ?
148 MENTAL ARITHHBTIC.
Lesson 4.
1. Mary having $51, paid $4^ for a hat, and the
rest for gloves ; what was the price of the gloves ?
2. From 8f take 5f ; from 7^ take 3f .
3. A lady went to a store with $20 and bought a
hat for $&J-, a fan for $1^, gloves for $lf, and boots
for $6f ; how much money had she left ?
4. A contractor, on Saturday night, paid out $100 :
to the mason he paid $25^, to the carpenter $18 ; what
sum was paid for lime, sand, and lumber, the bill for
which was settled with the remainder of the $100 ?
5. Three men buy a sailing vessel ; the first buys
^, the second ^, and the third the remainder ; what
part of the vessel did the third man buy ?
6. Fred wished to buy a tool chest worth $10.
After he had earned $7f , his mother made up the
remainder ; what did she give him ?
7. A milliner made 3 hats ; into the first she put f
of a yard of ribbon, into the second f of a yard, into
the third ^ of a yard. How many yards of ribbon
were put into the 3 hats ?
8. A sea-captain gave ^ of a ship to his son, f to
his daughter, and the remainder to his wife ; what
was the wife's share ?
9. Henry has $75J ; how much more money dbes
he need to buy a typewriter valued at $100 ?
10. A ship's crew of 15 men has provision for 3
months ; how many months will it last 1 man ?
11. A man gave 25 cents for his breakfast, which
was I of what he gave for his dinner ; what did he
give for his dinner ?
M£NTAL ARITHMETIC. 149
LeaBon 5.
1. A man paid $8f for fare, $3^ for hotel bill,
and $lf for carriage hire; what was the whole
outlay ?
2. A searcaptain owning ^ of a ship, bought from
his brother ^, and from his sister ^^ of the same
ship ; what part of the ship did he then own ?
3. A gentleman is 60 years old, and /^ of his age
is ^ of his wife's age ; how old is his wife ?
4. George had some money, and received J as
much from his father, which made the entire sum
$30 ; how much had he at first ?
5. A man sold a watch for $27, which was | of
what it cost him ; how much did he gain ?
6. Frank gave $24 for a chain, and paid for a
watch 2 J times as much as he paid for the chain ; how
much did the watch cost ?
7. Stephen earns $3^, and Samuel $4f in a week ;
how much will both earn in 1 week ? In 4 weeks ?
8. Harriet having 12 collars to make, has finished
I of them ; how many has she yet to finish ?
9. A cook-stove burns f of a ton of coal in a
month, and a furnace burns 9 times that amount;
how many tons does the furnace burn in a month ?
10. How many gallons of water will a crew of 12
men use in 20 days, if each man on the average uses
f of a gallon a day ?
11. George has ^ of a bushel of walnuts, and gives
^ of them to Eugene, and J of thfem to Richard;
what part of a bushel does George give to each of
his friends ?
150 MENTAL ARITHMETIC.
Le88on 6.
1. A man owning 15 acres of land gives -J- to his
wife, ^ to each of .his 3 daughters, and the rest to
his son ; how many acres does each receive ?
2. When potatoes are worth f 1-J^ a barrel, what
must be paid for i of a barrel ?
3. A boy with ^ of a peck of chestnuts gives -J- of
them to his mother, and i as many to his brother ;
what part of a peck does the brother receive ?
4. Samuel has 60 cents, i of which he spends for
candy and J of the remainder for a top ; how much
does he pay for the candy and the top ?
5. A man owtis a half-interest in a certain com-
pany, and gives his son J of his share ; what part of
the whole interest does the son receive ?
6. On a half-holiday Fritz gathered f of a bushel
of beech-nuts, while Hans gathered only f of that
quantity ; how many bushels did both gather ?
7. A man puts J of a car load of potatoes into 2
bins ; if he puts the same quantity in each bin, what
part of a car load is put into each bin ?
8. \ ot a, car load of potatoes just fills 2 bins ; if
one bin holds twice as much as the other, what part
of a car load is in each bin ?
9. If a horse travels ^^ of a mile in 6 minutes,
what distance will he go in 1 minute ?
10. When 3 bushels of apples cost f 2, what must
be paid for 8 bushels ?
11. A carpenter uses 3f bunches of shingles for
the roofs of 3 dormer-windows ; how many bunches
will be required to cover 7 such roofs ?
MENTAL ARITHMETIC. 151
LOBflOn 7.
1. A man buys a box of 200 oranges for 93 and
sells them at the rate of $^ a dozen ; how much does
he gain on each dozen ?
2. A coasting schooner carries 200 tons of coal at
$i a ton ; what is the freight on the coal ?
3. A gentleman left by will ^^^ of a ship to be
equally divided among his five sons ; what part of
the ship did each receive ?
4. How many yards of carpet at $f per yard can
be bought for $3i ?
5. When kerosene is 12^ cents a gallon, how many
gallons can be bought for 91 ?
6. A grocer gives 18 pounds of sugar for.$l; what
is the price per pound ?
7. A cubic foot of water weighs 1000 ounces and
a cubic foot of mercury weighs 13,600 ounces ; how
many times the weight of the water is the weight of
the mercury ?
8. A man received $2J per day, and a boy S»li per
day ; when the work was finished, they together
received $7 ; how many days did they work ?
9. A baker uses every day 4f barrels of flour ; how
long will 22 barrels last ?
10. A man can do ^ of a piece of work in 1 day,
and a boy can do J of it in 1 day ; how many days
will it take each alone to do it ?
11. A mason saves every month $7}, and a car-
penter $8f ; what is the sum of their savings ?
12. At 50 cents a ^' cut " what will it cost to saw
each stick in a cord of wood into 3 pieces ?
152 MENTAL AKITHMETIO.
Lefloon 8.
1. A coat costs 9^0, a hat $3, and a pair of shoes
95^. How much will be left of $50 after paying
for the above named articles ?
2. A freight-train running 15 miles an hour is 48
miles in advance of an express-train running 31 miles
per hour ; in how many hours will the express over-
take the freight-train ?
3. From a gallon of molasses a cook uses J of a
gallon, and J of the remainder leaks away; how
much molasses remains ?
4. A tug-boat burns 2J tons of coal per day; If
the coal costs f 4J per ton, how much will it cost to
run the boat for 6 days ?
5. A steamer sails due south at the rate of 15^
miles per hour ; a brig starting at the same time and
from the same place as the steamer sails due north
at the rate of 9f miles per hour ; how far apart will
the two vessels be at the end of 1 hour ?
6. After 4f years Robert will be 15 years old;
what is his present age ?
7. A man hired 4 men and at the end of a week
paid $60 to them ; to the first he gave $15, to the
second f of the remainder, to the third $8 ; how
many dollars did he give the fourth man ?
8. A man having some wheat gave it to 6 poor
persons, giving each f of a bushel; how many bushels
did he distribute?
9. How much cloth at $lf per yard can be bought
for $9? for $10? for $12 ? for $16? for $18? for
$21 ? for $28 ? for $49 ? for $56 ?
UENTAIi ABITHMETIC. 163
Lesaon 9.
1. A farmer exchanged 8 pounds of butter, worth
$i per pound, for 3 pounds of tea at $f , and some
sugar ; what was the value of the sugar received ?
2. George has $^ ; his father gives him i of that
amount, and his mother enough to make up $1 ; what
part of $1 does his mother give him?
3. A lady used f of a roll of carpeting for her
drawing-room, ^ for her music-room, and the rest, 12
yards, for her study ; how many yards in the roll ?
How many yards were used for the drawing-room ?
4. How many yards of carpeting 3 feet wide will
it take to carpet a room 30 feet long by 20 feet wide
if the strips run across the room ?
5. A lady buys 5 yards of lace at $H per yard,
10 yards of muslin at $1 per yard, and pays $1^ for
trimmings ; how many dollars does she spend ?
6. A gentleman sold some railway stock for $320
and gave ^ of this sum to his daughter, J of it to
his niece, and the remainder to his son; how many
dollars did each receive ?
7. How many barrels each holding 2i bushels will
be required to hold 10 bushels of potatoes ?
8. What is the difference in cost between 6 yards
of lace at $1^ per yard and a barrel of flour at $5^ ?
9. If a man spends $lf a day, how many dollars
will he spend in 7 days ? .
10. How many one-ounce bullets can be made from
6J pounds of lead ?
U. When zinc is worth 6 cents a pound, how
many pounds can be bought for $1^ ?
154 MENTAL ARITHMETIC.
Lesson 10.
1. A man's house lot is 50 feet wide and 70 feet
deep ; how many square feet in the lot ?
2. A piece of cloth is 5 yards long and 1 yard
wide ; how many square feet of cloth in the piece ?
3. A pane of glass is 10 inches long and 8^ inches
wide ; how many square inches in the pane ?
4. When potatoes are worth $f a bushel, what
part of a dollar is a peck worth ?
5. If a family consumes 2 pounds 3 ounces of meat
in a day, how much will the family consume in a
week?
6. A schooner carries 250 tons of coal at 91 per
ton from New York to Portsmouth ; if $50 is de-
ducted for wharfage and the captain receives f of the
remainder, what sum will the owners of the schooner
receive ?
7. How many square feet in a board 6 feet long
and 2i feet wide ?
8. How many cubic feet in a pile of earth 8 feet
long, 4 feet wide, and 2^ feet high ?
9. At 3 cents a pint what must be paid for 6^
quarts of milk?
10. If potatoes are bought for 50 cents a bushel,
what will be the gain on 5 bushels sold at the rate of
20 cents a peck ?
11. How many quart baskets will be required to
take to market 3^ pecks of strawberries ?
12. When strawberries are worth 10 cents a quart
at wholesale, how many dollars will be made on 1
bushel 1 peck at 15 cents per quart at retail ?
MENTAL ARITHMETIC. 155
LesBon 11.
1. Wlien sugar is worth 5 cents a pound, how
many dozen eggs at 25 cents a dozen will pay for 20
pounds of sugar ?
2. When sugar is worth 6J cents a pound, how
many dozen eggs at 25 cents a dozen will pay for 20
pounds of sugar ?
3. How many bushels of potatoes at $J a bushel
must be given for 10 yards of cloth at $3f per yard ?
4. James gave away 4 cents, which was J of all
he had ; how many cents had he at first ?
5. Mary gave 3 oranges to Susan and 5 to Ellen,
she then found that she had given away f of all she
had ; how many had she left ?
6. A boy walking at the rate of 3 miles an hour is
8 miles in advance of a man following at the rate of
5 miles an hour ; in how many hours will the man
overtake the boy ?
7. A lady cut from a piece of calico, containing 40
yards, 12^ yards for a dress, 7| yards for aprons,
8f yards for curtains ; how many yards were Igft ?
8. A man bought a horse for $125, and after keep-
ing him 3 weeks at $4^ per week, sold him for $150;
how many dollars did he gain ?
9. A young man owning f of a ship, sold i of his
share ; if the whole ship was worth $24,000, how
many dollars did he receive ?
10. How many yards of carpet 1 yard wide will
be needed for a room 24 feet long by 18 feet wide ?
11. Which is the greater, i of 10^ or ^ of 24 ?
12. Which is the smaller, f of 16 or J^ of 62 ?
156 MENTAL ARITHMETIO.
LOBSon 12.
1. Mary does f of a piece of sewing in a day,
while Jane does -J- of it ; how much more is accom-
plished by Mary than by Jane ? In what time will
the work be completed if both work together ?
2. A young man spent $60 for a typewriter,
which sum was f of all the money he had ; how
many dollars had he after making the purchase ?
3. Said George to Henry, " If you add to my age
f of it, and 7 years, the sum will be 35 ; how old
ami?"
4. A school-teacher receives a salary of $1500 for
9 months' work, while an engraver receives a salary
of $1200 for 12 months' work ; how many more dol-
lars per month of work does the teacher receive than
the engraver ?
5. In a school f of the pupils study Latin, -J- study
French, and the remainder, 12, study English Gram-
mar ; how many scholars make up the school ?
6. A farmer sold ^ of a flock of sheep to the
butcher, and i of the remainder to a neighbor, and
still had 50 ; what was the original number ?
7. At a " mark-down" sale a lady bought a hat for
$5, but as the hat was out of style she paid $6 to have
it made over; had she bought it in the beginning of the
season, the hat would have cost $9.50 ; did she gain
or lose by the purchase, and how much ?
8. A gentleman bought a bond for $1010 ; a year
later he sold the bond for $1080. If he paid $60.06
for the use of the money and received $50 interest
on the bond, how much did he gain ?
MENTAL ABITHMETIC. 167
Lesson 13.
1. A gentleman gave ^ of his property to his wife,
■J- of the remainder to his daughter, and divided the
property left equally among his three sons; what
part of the property was received by each son ?
2. A fruit dealer bought 10 boxes of oranges at
$3.25 a box and sold the lot for $50 ; how many dol-
lars did he gain per box ?
3. At a certain hour a pole 4^ feet long casts
a shadow of 9 feet ; what is the length of a chimney
casting a shadow of 63 feet at the same time ?
4. A pole has -J- of its length in water and the re-
mainder of its length, 14 feet, in the air ; bow long is
the pole ?
5. A pole has ^ of its length in mud, f of its
length in water, and the remainder of its length,
2 feet, in the air ; how many feet long is the pole ?
6. What will a boy earn in 9 days, if he receives
$3 for working 5 days ?
7. If a boy takes 11 steps in walking 16^ feet, how
many steps will he take in walking 8 rods ?
8. How many times can a pint measure be filled
from a basket of chestnuts containing 3^ pecks?
For how much money will the chestnuts retail at 5
cents a pint ?
9. Maud and Belle have together $270 in the
Savings Bank, and Belle's deposit is IJ times that
of Maud ; how many dollars has each in the bank ?
10. A second-hand piano cost $60 ; f of the price
of the piano was equal to 8 times the cost of the
piano-stool ; how many dollars did the stool cost?
158 MENTAL ARITHMETIC.
Lesson 14.
1. Ten are how many times eight ?
2. Eleven are how many times eight ?
3. Twelve are how many times eight ?
4. Thirteen are how many times eight ?
5. Fourteen are how many times eight ?
6. Fifteen are how many times eight ?
7. Sixteen are how many times twelve ?
8. Seventeen are how. many times twelve?
9. Eighteen are how many times twelve ?
10. Nineteen are how many times twelve?
11. Twenty are how many times twelve ?
12. Twenty-one are how many times twelve ?
13. Twenty-two are how many times twelve ?
14. Twenty-three are how many times twelve ?
15. Twenty-four are how many times sixteen ?
16. Twenty-five are how many times sixteen ?
17. Twenty-six are how many times sixteen ?
18. Twenty-seven are how many times sixteen ?
19. Twenty-eight are how many times sixteen ?
20. Twenty-nine are how many times sixteen ?
21. Thirty are how many times sixteen ?
22. Thirty-one are how many times sixteen ?
23. Thirty-two are how many times five ?
24. Thirty-three are how many times five ?
25. Thirty-four are how many times five ?
26. Thirty-five are how many times six ?
27. Thirty-six are how many times six ?
28. Thirty-seven are how many times six ?
29. Thirty-eight are how many times six ?
30. Thirty-nine are how many times six?
MEKTAL ABITHMETIC. 159
Iieflflon 15.
1. Fifty are how many times 7?5?9?4?6?
2. Forty-four are how many times 3?4?6?9?
3. Sixty-four are how many times 8?6?4?9?
4. Seventy-four are how many times 10?8?6?7?
5. Forty-six are how many times 5?6?8?4?9?
6. Fifty-six are how many times 6? 7? 5?9?10?
7. Sixty-six are how many times 4?9?8?6?
8. Seventy-six are how many times 4?6?6?8?
9. Fifty-two are how many times 8? 6? 5?4?3?
10. Fifty-two are how many times 6?8?4?6?12?
11. Sixty-two are how many times 9? 8?3?4?5?
12. Seventy-two are how many times 10?8?6?3?
13. Forty-eight are how many times 9?8?7?6?
14. Fifty-eight are how many times 6?8?9?5?
15. Sixty-eight are how many times 5? 8? 9? 12?
16. Seventy-eight are how many times 6?9?8?4?
17. Eighty-two are how many times 6?8?9?4?3?
18. Ninety-two are how many times 8?6?9?6?
19. Eighty-four are how many times 8?6?4?5?
20. Ninety-four are how many times 6?9?8?4?
21. Eighty-six are how many times 6?7?8?4?
22. Ninety-six are how many times 4?8?9?3?
23. Eighty-eight are how many times 5?6?9?8?
24. Ninety-eight are how many times 4?8? 3? 9?
25. Forty-five are how many times 4?6?8?12?
26. Fifty-five are how many tim«s 3?4?6?9?8?
27. Sixty-five are how many times 6? 8? 6?4?9?
28. Seventy-five are how many times 6?7?8?4?
29. Eighty-five are how many times 6?7?9?4?
30. Ninety-five are how many times 6?8?9?4?
160 MENTAL ARITHMETIC.
Leraon 16.
1. In 3 and 2 fourths how many fourths ?
2. In 4 and 3 fourths how many fourths ?
3. In 5 and 1 fourth how many fourths ?
4. In 6 and 2 thirds how many thirds ?
5. In 7 and 1 third how many thirds ?
6. In 8 and 2 fifths how Inany fifths ?
7. In 9 and 3 fifths how many fifths ?
8. In 12 and 1 fifth how many fifths ?
9. In 7 and 3 eighths how many eighths ?
10. In 2 and 5 eighths how many eighths ?
11. In 3 and 2 eighths how many eighths ?
12. In 2 and 6 sixteenths how many sixteenths ?
13. In 5 and 3 sixteenths how many sixteenths ?
14. In 4 and 7 sixteenths how many sixteenths ?
15. In 1 and 9 sixteenths how many sixteenths ?
16. In 3 and 4 sixteenths how many sixteenths ?
17. In 1 and 7 twelfths how many twelfths ?
18. In 3 and 2 twelfths how many twelfths ?
19. In 5 and 7 twelfths how many twelfths ?
20. In 4 and 3 twelfths how many twelfths ?
21. In 6 and 9 twelfths how many twelfths ?
22. In 3 and 7 tenths how many tenths ?
23. In 6 and 8 tenths how many tenths ?
24. In 8 and 4 tenths how many tenths ?
25. In 2 and 5 ninths how many ninths ?
26. In 1 and 7 ninths how many ninths ?
27. In 2 and 7 twenty-fifths how many twenty-fifths ?
28. In 3 and 6 twenty-fifths how many twenty-fifths ?
29. In 4 and 24 twenty-fifths how many twenty-fifths ?
30. In 5 and 9 twenty-fifths how many twenty-fifths ?
MENTAL ABITHMETIC.
161
laesaon 17.
1. f of 28 is f of what number ?
2. f of 16 is f of what number ?
3. I of 36 is I of what number ?
4. -/y of 48 is J of what number ?
5. 1*^^ of 36 is ^ of what number?
6. ^ of 56 is J of what number ?
7. -^ of 30 is f^ of what number?
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
^^ of 26
^ of 64 is ^ of what number ?
J of 27 is -/t of what number ?
is f*j of what number?
j»^ of 30 is f of what number ?
I of 42 is ^ of what number ?
^ of 64 is f of what number ?
I of 32 is J of what number ?
J of 75 is ^^ of what number ?
f of 56 is I of what number ?
5 of 72 is ^^ of what number ?
John has 25% more money than William.
William's money is what per cent of John's money ?
19. A man sold a horse for $240 and gained 20%
of the cost. What did the horse cost ?
20. A man sold a horse for $220 and lost 8^% of
the cost. What did he pay for the horse?
21. If 80% of a lot of lumber is sold, what per cent
of the lumber is not sold ?
22. If there is a loss of 16|-% on the cost, when
velvet is sold for $10 a yard, what is the cost of the
velvet a yard?
23. A man sold a wagon for $50, and lost 37^% of
the cost. What was the cost of the wagon ?
162 MENTAL ARITHMETIC.
ZiesBon 18.
1. What part of a number is 10% of it ?
2. What part of 10% is 1% ?
3. What is the meaning of 1% of a number ? 2%?
3%? 6%? 6%?
4. What fraction, in its lowest terms, expresses
the value of 2%? 4%? 5%? 6%? 8%? 12%?
5. What per cent of a number is j^j^ of it ? j^jf ?
A? A? lAr? 3^? A^ijV? iftr?
How much is :
6. 1 % of 200 houses ? 14. 12% of 25 days?
7. 2% of 60 sheep ? 15. 6% of 60 lb. ?
8. 3% of 100 men ? 16. 4% of 260 bu.?
9. 6% of 80 trees ? 17. 1% of 260 bu. ?
10. 4% of 76 books ? 18. 6% of 300 yd. ?
11. 6% of 160 horses ? 19. 2% of $360 ?
12. 8% of 26 boats ? 20. 30% of 90 men ?
13. 7% of $400 ? 21. 16% of 400 gal. ?
22. 3 is 6% of a number. What is the number ?
23. Mr. Brown drew 4% of his deposit in a
savings bank. If he drew $10, how much had he in
the bank at first ?
24. What per cent of a number is ^ of it ?
25. How many years in 16% of a score of years ?
26. 7% of a regiment of 1000 u^en were wounded.
How many men were wounded ?
27. 18 is 9% of what number ?
28. If 16% of the inhabitants of a town are
voters, and there are 960 voters, how many inhabit-
ants are there in the town ?
MENTAL ARITHMETIC. 163
Leraon 19.
1. What part of 100 is 12i ? 37^? 62^? 87^?
2. How many dollars are there in 12^^ of $24 ?
37i% of f 24 ? 62i% of $24 ? 87^% of $24 ?
3. How many ounces are there in 12^^ of 1 lb. ?
in37i%of lib.?
4. John gave away f of his marbles. What per
cent of his marbles did he give away ?
5. If 11 peaches are 12^^ of the peaches in a
basket, how many peaches are there in the basket?
6. A farmer mowed 37^^ of a field containing 24
acres. How many acres did he mow ?
7. After selling 12^^ of his geese, a farmer had
28 geese left. How many geese had he at first ?
8. What per cent of a number is | of it ? ^ ? ^j^ ? f ?
9. What is l^% of $35 ? 28^% ? 67|% ?
10. What is 14f % of 10 rd. ? 42f % of 10 rd. ?
11. A bought ^ of a field and 6 ^ of it. What per
cent of the field did each buy ?
12. A owns Si^o a.nd B 25% of a field. B's share
is how many times A's share ?
13. What part of 12^ is 6^ ? What per cent ?
14. What part of an acre is 6^% of an acre ?
15. What per cent of a pound is ^ of a pound ?
16. How many square inches are there in 6J% of
a square foot ? 11J% ? 22f % ?
17. How many square feet are there in 11^% of a
square yd? 22f%?
18. What per cent of a sum of money will each
receive, if it is divided equally among 6 men ? 8 men ?
16 men? 9 men ? 7 men? 12 men?
164 MENTAL ARITHMETIC.
Lesson 20.
How mnch is :
1. 60% of 36 gal. ? 30. 70% of 40 ?
2. 25% of 44 qt. ? 31. 80% of 30 ?
3. 20% of 75 A. ? 32. 90% of 60 ?
4. 10% of 26 lb. ? 33. 60% of 70 ?
6. 10% of $60 ? 34. 8% of 460 ?
6. 30% of $60 ? 35. 6% of 160 ?
7. 33i% of 42 rd. ? 36. 6% of 260 ?
8. 33i% of 64 sheep ? 37. 6% of 300 ?
9. 66f % of 27 ducks ? 38. 6% of 600 ?
10. 100% of 36 mi. ? 39. 26% of 96 ?
11. 16f % of 48 yd. ? 40. 25% of 800 ?
12. 16f % of 7 lb. ? 41. 12^% of 800 ?
13. 8i% of 24 horses ? 42. 12^% of 88 ?
14. 8i% of $60 ? 43. 33i% of 63 ?
15. 12^^% of 32 qt. ? 44. 16f % of 63 ?
16. 12i% of 64 cows ? 45. 66^% of 63 ?
17. 37i% of 40 boys ? 46. 33^% of 270 ?
18. 87i% of 40 girls ? 47. 60% of i lb. ?
19. 62^% of 66 children ? 48. 60% of i gal. ?
20. 6i% of 32 ft. ? 49. 25% of i bu. ?
21. 18f % of 16 oz.? 50. 25% of f mi. ?
22. 11^% of 18 sq. ft. ? 51. 20% of ^ rd. ?
23. 22f % of 36 boxes? 52. 20% of ^ A. ?
24. 14f % of 21 cwt. ? 53. 33^% of -J- ft. ?
25. 28^% of $36 ? 54. 66f % of i mi.?
26. 6% of 120 geese ? 55. 12^% of i lb. ?
27. 4% of 160 oxen ? 56. 26% of J ft. ?
28. 2% of 60 cents ? 57. 60% of f sq. ft. ?
29. 3% of 600 men ? 58. 20% of 1 1- ?
MENTAL ABITHMETIC. 105
Iiesaoii 21.
1. What per cent of a number is J of the number ?
i of the number ? the whole number ? -
2. If 10% of a number is taken away, what per
cent is left ?
3. A's horse is worth 10% less than B's. If B's
horse is worth $200, what is A's worth ?
4. If a sleigh cost $60, what will it be worth after
its value has decreased 25^o^
6. William bought 45 marbles and lost 33 J % of
them ; what part had he left ? how many marbles ?
6. John picked 12 qt. of berries and James 25%
more than John ; how many quarts did James pick ?
7. What number is 125% of 12 ?
8. What number is 25% greater than 12?
9. What number is 120% of 25 ?
10. j of a number is what per cent of the number ?
11. f of a number is what per cent of the number ?
12. 150% of a number is what fraction of the
number ?
13. 112^% of a number is what fraction of the
number ?
What number is ;
14. 20% less than 35 ? 22. 12^% more than 48 ?
15. 25% less than 44 ? 23. 12^% less than 48?
16. 33i% less than 54 ? 24. 25 % more than 60 ?
17. 16|% less than 36? 25. 10% less than 180?
18. 12^% less than 32 ? 26. 16f % more than 72 ?
19. 50% less than 400? 27. 33^% more than 240?
20. 50% more than 400? 28. 40% more than 25?
21. 25% more than 80? 29. 14]^% more than 28?
166 MENTAL ARITHMETIC.
LeBson 22.
1. What part of 90 is 30 ? what per cent ?
2. What part of 10 is 6f ? what per cent ?-
What per cent of ;
3. 80 oz. are 20 oz.? 11. 42 is 6 ?
4. 30 lb. are 9 lb.? 12. 45 is 6?
6. 26 yd. are 5 yd.? 13. 30 is 21 ?
6. 60 cows are 20 cows ? 14. 24 is 18 ?
7. 60 min. are 10 min.? 15. 20 is 30 ?
8. 36 in. are 24 in:? 16. 12 is 16?
9. 24 eggs are 3 eggs ? 17. 28 is 35 ?
10. 144 in. are 108 in.? 18. 25 is 30?
19. A boy picked 15 qt. of blackberries, and sold
12 qt. ; what per cent of his berries did he sell ?
20. 10 oz. of oil are mixed with 5 oz. of turpen-
tine ; what per cent of the mixture is oil ?
21. From a barrel containing 32 gal. of oil 4 gal.
leaked out ; what per cent of the oil leaked out ?
22. In a grove containing 60 trees there are 45
pines ; what per cent of the grove are pines ?
23. A has $7^, and B has $30 ; A's money is what
per cent of B's ?
24. If 16 lb. of gunpowder contain 3 J lb. of sul-
phur ; what per cent of the gunpowder is sulphur ?
25. If 8 lb. of lead, 7 lb. of zinc, and 6 lb. of tin
are melted together, what per cent of the mixture is
tin ? What per cent of the mixture is zinc ?
26. An agent was given bills to collect amounting
to $65. He collected $32.50 ; what per cent of the
amount of the bills did he collect ?
MENTAL ABITHMETIG. 167
Lesson 23.
1. 9 is f of what number ? 75% of what number ?
2. $15 is I of what ? 83^% of what?
3. If 20 is 66J% of a number, what part of the
number is 20 ? What is the number ?
4. If 16 is 80% of a number, what is the number ?
What is the number of which :
5.
13 is 20%?
11.
11 is 16f %?
6.
100 is 25%? •
12.
2 is 4%?
7.
22i8 33i%?-
13.
7 is 6%?
8.
22 is 40%?
14.
12 is 6%?
9.
21is37i%?
15.
300 is 30%?
10.
35 is 50%?
16.
64 is 90%?
17. 20 is J of what number ? ^ more than what
number ? 33^% more than what number ?'
18. If 30 is 25% more than a number, what per
cent of the number is 30 ? What fraction of the num-
ber is 30 ? What is the number ?
19. If 24 is 20% less than a number, what per
cent of the number is 24 ? What fraction of the num-
ber is 24 ? What is the number ?
20. 28 is 30% less than what number ?
21. 22 is 10% more than what number?
What is the number of which :
22.
24 is 160%?
27.
48 is 120%?
23.
27 is 112^%?
28.
49 is 176%?
24.
32 is 133i%?
29.
42 ^ 116J%?
25.
26 is 166J%?
30.
28 is 140%?
26.
40 is 125%?
31.
22 is 137i%?
168 MBNTAL ABITUMETIG.
Lesson 24.
1. What is the interest on iP260 for 1 year at 6% ?
2. What is the interest on $300 for 2 months at
6% a year?
3. What is the interest on $50 for 6 months at
4% a year?
4. What is the interest on $50 for 4 months at
6% a year?
6. What is the interest on $3600 for 30 days at
4% a year?
Note. In interest problems we reckon 30 days as a month,
and 360 days as a year ?
6. What part of a year are 30 days ? 60 days ?
90 days ? 120 days ? 150 days ? 180 days ?
7. What part of a month are 5 days ? 3 days ?
6 days ? 10 days ? 15 days ? 20 days ?
What is the interest on
8. $1000 for 30 days at 6% ?
9. $1000 for 60 days at 4^% ?
10. $500 for 90 days at 4% ?
11. $400 for 1 month and 6 days at 5% ?
12. $1200 for 2 months and 15 days at 5% ?
13. $1200 for 3 months and 10 days at 4% ?
14. $1200 for 4 months and 3 days at 3% ?
,15. $600 for 6 months and 20 days at 5% ?
16. $60a for 8 months and 10 days at 6% ?
17. $600 for 1 year and 4 months at 4% ?
18. $500 for 2 years and 3 months at 4% ?
19. $3600 for 3 months and 5 days at 4% ?
20. $3000 for 2 months and 21 days at 4% ?
MENTAL ARITHMETIC. 169
IieMon 25.
1. The population of a town decreased 20% and
was then 720. What was the number of inhabitants
before the decrease ?
2. A piece of cloth after shrinking 5% was 38
yds. long. How long was it before shrinking ?
3. 66i^o of tte contents of a bottle of ether evap-
orated. It then contained 4 oz. How many ounces
were in the bottle at first ?
4. A man having paid 87^% of his debts still owed
$20. How much did he owe at first ?
5. By selling newspapers a boy increased the
amount of money that he had 20%. He then had 60
cents. How much did he have at first ?
6. A farmer was offered $30 for a cow, which was
75% of his price. How much did he ask for the cow ?
7. A coal dealer sold 30% of a cargo of coal and
had 280 tons left. How many tons in the cargo ?
8. A man bought 40% of a vessel for $2000.
What was the value of the vessel at the same rate ?
9. 60% of the scholars of a school are girls. If
there are 42 girls in the school, how many boys are
there in the school ?
10. After a 10% reduction in wages a man was
paid $9 a week. What was his weekly pay before
the reduction ?
11. 54 is 12|^% more than what number?
12. 49 is 12^% less than what number?
^ 13. 160 is 33^% more than what number?
14. 120 is 66f % more than what number ?
15. 15 is 40% less than what number?
170 MENTAL ARITHMETIC.
LesBon 26.
1. If cloth costing $5 was sold for $7, how many
dollars were gained ? What per cent of $5 is $2 ?
What was the per cent of profit ?
2. If silk costing $12 was sold for $10, how many
dollars were lost? What per cent of $12 is $2?
What was the per cent of loss ?
Note. The Rate of Profit or Loss is the per cent the profit
or loss is of the Cost Price,
What is the rate of profit or loss : —
3. If goods costing $100 are sold for $120?
4. If goods costing $140 are sold for $160?
5. If goods costing $250 are sold for $300 ?
6. If goods costing $120 are sold for $140 ?
7. If goods costing $180 are sold for $189 ?
8. If goods costing $120 are sold for $100 ?
9. If goods costing $30 are sold for $24 ?
10. If goods costing $42 are sold for $36 ?
11. If goods costing $3§ are sold for $28 ?
12. If goods costing $50 are sold for $42 ?
13. A canoe which cost $40 was sold for $36.
What was the per cent of loss ?
14. If a man buys corn at 45 cents a bushel and
sells it at 50 cents, what per cent does he gain ?
15. A man bought a 9-pound turkey for $1.50
and sold it for 20 cents a pound. What was the
rate of gain ?
16. A piece of cloth containing 40 yd. was bought
for $3 and sold at the rate of 10 cents a yard. What
was the rate of profit?
MENTAL ARITHMETIC. 171
Lesson 27.
What is the rate of profit or loss:
1. If goods costing $^ are sold for $} ?
2. If goods costing $1 are sold for $f ?
3. If goods costing f ^ are sold for $1 ?
4. If goods costing $1 are sold for $-J- ?
6. If goods costing $i are sold for $i ?
6. If goods costing $^ are sold for $^ ?
7. If goods costing $f are sold for $^ ?
8. If goods costing $f are sold for f f ?
9. If goods costing $^ are sold for $f ?
10. If goods costing $i are sold for $^ ?
11. If a bbl. of flour costing $4 is sold for $4.60 ?
12. If a ton of coal costing $3 is sold for $3.75 ?
13. If a ton of coal costing $5 is sold for $4.50 ?
14. If a cd. of wood costing $5 is sold for $6.25 ?
15. If a cd. of wood costing $3.50 is sold for $3 ?
16. If beef costing 15 cents a lb. is sold for 18
cents a lb. ?
17. If chickens costing 18 cents a lb. are sold for
20 cents a lb. ?
18. If a house costing $2000 is sold for $1400 ?
19. If a farm costing $4500 is sold for $6000 ?
20. If a vessel costing $7000 is sold for $6500 ?
21. If a carriage costing $125 is sold for $75 ?
22. If a boat costing $90 is sold for $75 ?
23. If a patent costing $1000 is sold for $2500 ?
24. If a house-lot costing $750 is sold for $1000 ?
25. If a bond costing $800 is sold for $1100 ?
26. If a saw-mill costing $1200 is sold for $2000 ?
27. If a horse costing $375 is sold for $250 ?
172 MENTAL ARITHMETIC.
Lesson 28.
1. If goods costing $20 are sold at 10^ profit,
what is tlie profit ? What is the selling price ?
2. If goods costing $12 are sold at 25o/c loss,
what is the loss ? What is the selling price ?
What is the selling price :
3. When goods costing $60 are sold at 20% profit ?
4. When goods costing $80 are sold at 50% profit ?
5. When goods costing $120 are sold at 25o/o loss ?
6. When goods costing $50 are sold at 6% loss ?
7. When goods costing $200 are sold at 5% loss ?
8. When goods costing $48 are sold at 12^ % profit ?
9. When goods costing $200 are sold at 10% loss ?
10. When goods costing $600 are sold at 33^% loss ?
11. When goods costing $28 are sold at 14f % profit?
12. Wheti goods costing $42 are sold at 16|- % profit?
13. When goods costing $75 are sold at 4% loss ?
14. When goods costing $200 are sold at 3% loss ?
15. When goods costing $400 are sold at 1 % loss ?
16. When goods costing $100 are sold at 100%
profit?
17. When goods costing $500 are sold at 25 % profit?
18. When goods costing $300 are sold at 66f %
profit ?
19. A piece of cloth containing 20 yd. was bought
for 8 cents a yard; what must be charged for the
whole piece, if a profit of 25% is to be made ?
20. A piece of silk containing 12 yd. was bought
for $18. It was sold at a loss of 16f %; what was
the selUng price per yard ?
MENTAL ARITHMETIC. 173
Leraon 29.
Ex. 1. If goods are sold for f 140 at a profit of
16f %, what is the cost of the goods ?
Since the profit is ICf % of the cost, the profit is J of the cost.
Therefore the selling price is J of the cost. Hence, J of the cost
is ^ of $140, or $20 ; and } of the cost is 6 X $20, or $120. Ans.
What is the cost :
1. When goods are sold for $20 at a profit of 25%?
2. When goods are sold for $14 at a profit of 16f % ?
3. When goods are sold for $42 at a loss of 12^%?
4. When goods are sold for $80 at a loss of 33^%?
6. When goods are sold for $72 at a loss of 10%?
6. When goods are sold for $25 at a profit of 66f % ?
7. When goods are sold for $55 at a profit of 37^% ?
8. When goods are sold for $50 at a profit of 100 % ?
9. When goods are sold for $60 at a loss of 20%?
10. When goods are sold for $52 at a profit of 4% ?
11. By selling a horse for $140 a dealer lost 12^% ;
what was the cost of the horse ?
12. Henry sold a book-case for $15 and lost 16|% ;
what was the cost of the book-case ?
13. By selling cloth at 18 cents a yard there is
a profit of 12^%; what is the cost per yard ?
14. If 20% is gained by selling sugar at 6 cents a
pound, what is the cost of sugar a pound ?
15. If there is a loss of 20% by selling butter at
16 cents a pound, what is the cost a pound ?
16. If there is a profit of 12^% in selling a pig
for $9, what is the cost of the pig ?
17. If there is a loss of 10% in selling a pig for •
, what is the cost of the pig?
174 MENTAL ABITHMBTIC.
Leiwon 30.
1. 8 is ^ of what number ? 8 is 20 % of what num-
ber? If a profit of $8 is a profit of 20%, what is
the cost ? What is the selling price ?
What is the cost and the selling price :
2. When a gain of $20 is a gain of 50% ?
- 3. When a gain of $5 is a gain of 25% ?
4. When a gain of $7^ is a gain of 25% ?
5. When a gain of $2 J is a gain of 20% ?
6. When a gain of $13 is a gain of 10% ?
7. When a gain of $30 is a gain of 66|% ?
8. When a loss of $70 is a loss of 33^% ?
9. When a loss of $90 is a loss of 75% ?
10. When a loss of $12 is a loss of 37^% ?
11. When a gain of $28 is a gain of 40% ?
12. When a loss of $45 is a loss of 90% ?
13. When a loss of $48 is a loss of 80% ?
14. When a gain of $15 is a gain of 16f % ?
15. When a gain of $3J is a gain of 12^% ?
16. A 4% investment pays $20 a year; what is
the amount invested ?
17. A man receives $60 from a 5% investment
and $80 from a 4% investment; how much has he
in each investment ?
18. A bankrupt paid his creditors 40% of their
claims. Mr. C. received $200 ;' what was the amount
of his claim ?
19. How much money must be invested in a sav-
ings bank, paying 3% yearly, to get a yearly income
of $21 ?
MENTAL ARITHMETIC. 175
I«MK>I1 31.
1. 10 is what part of 50 ? what per cent of 50 ?
2. By an inyestment of $50 a man gained $10.
What per cent did he gain ?
What per cent is received :
3. When an investment costing $60 pays $6 ?
4. When an investment costing $90 pays $9 ?
5. When an investment costing $120 pays $6 ?
6. When an investment costing $80 pays $5 ?
7. When an investment costing $40 pays $2 ?
8. When an investment costing $100 pays $4^?
9. When an investment costing $100 pays $3^ ?
Shares in railroads, banks, etc., usually have a par value of
$100. By par value is meant the sum stated on the certificate
of stock for each share. Dividends are paid on the par wlue.
Counting the par value $100, what is the yearly
income :
10. From 1 share paying 4% a year ?
11. From 5 shares paying 3% a year ?
12. From 12 shares paying 2 j-% a year ?
13. From 8 shares paying 5% a year ?
14. From 20 shares paying 7% a year?
15. If a share of stock paying 5% a year is
bought for $50, what per cent of his investment does
the buyer receive each year ?
Whatiper cent is received :
16. From an 8% stock bought for $80 a share ?
17. From a 3^ stock bought for $50 a share ?
176 MBNTAL ABITHMBTIC.
Ziesson 32.
1. An agent bought f 1000 worth of cotton. What
was the amount of his commission at 3% ?
2. An agent sold a house for $8000. What was
his commission at 2^% ?
3. How much would a tax collector receive for col-
lecting $20,000, if his commission was 1J% ?
4. An agent sold a horse for $500. How much
would the owner receive, if 4% was charged for com-
mission and expenses ?
5. An agent charged $3 for collecting $100.
What was his rate of commission?
6. An agent sold a house for $5000 ^nd after de-
ducting his commission gave the owner $4900. What
was his rate of commission ?
7. If money is sent an agent to buy grain and his
commission is 2% of the sum paid for grain, what
sum must be sent to buy $100 worth of grain ?
8. In the last example, what sum can he invest in
grain, if he receives $1.02 ? $5.10 ? $102 ? $306 ?
$816? $1020?
9. A merchant sent his agent $515 to invest in
flour at $5 a barrel. If the agent's commission is
3% of the sum paid for flour, how many barrels of
flour can he buy ?
10. An agent received $2100 to buy cotton. If
the agent's commission is 5% on the sum paid for
cotton, what sum can he invest in cotton? How
much is his commission ?
U. An agent sold a house for $5000. How much
is his commission at 3)^^ ?
MENTAL ABITHMBTIC. 177
Leaaon 33.
1. If a house is insured for $1000 and the insur-
ance company charges 1% a year for insuring the
house, what is the annual charge, or premium ?
2. What is the premium of insurance for $500 on
a house at 1^% ?
3. What is the premium of insurance for $2500 on
a house at i of 1% ?
4. What is the premium of insurance for $3000 on
a steam mill at 5^ ?
5. A building worth $8000 is insured at f of its
value for ^ of 1 % per annum. What is the annual
premium ?
6. A building worth $6000 is insured at f of its
value for f of 1 % per annum. What is the annual
premium ?
7. The premium of insurance at 1% is $15. What
is the amount insured ?
8. The premium of insurance at 1|% is $18.
What is the amount insured ?
9. What is the annual premium of fire insurance
for $2640 at i of 1%?
10. What is the annual premium of fire insurance
for $3200 at J of 1%?
11. The premium of insurance at ^ of 1^ is $12.
What is the amount insured ?
12. The yearly premium for insuring a house for
$6000 is $30. What is the yearly rate of insurance ?
13. Mr. Brown paid $60 to insure his house for
$4000 for 5 years. What was the yearly rate of in-
surance ?
178 MENTAL ARITHMETIC.
LeBBon 34.
XHscouvi is a reduction from the amount of a bill of goods,
and is usually reckoned at a per cent off. Often two or more
successive discounts are made from the list prices of goods. In
such cases the first discount is made from the list price ; the
second discount is made from the. remainder, and so on.
Ex. 1. What is the net cost of a bill of goods
amounting to $500; subject to 20 off ?
Solution: 20% of $500 = ^ of $600 = |100, the discount;
and $500 — $100 = $400, net cost.
Ex. 2. What is the net cost of a bill of goods
amounting to $400 and subject to 25 and 10 off?
Solution : 26% of $400 = ^ of $400= $100, $400 - $100 = $300;
10% of $300 = ^c of $300 = $30, $300 — $30 = $270, net cost.
*What is the net cost of goods billed at :
1. $150 with 10 off ? 8. $750 with 20 and 5 off ?
2. $250 with 20 off? 9. $240 with 25 and 10 off?
3. $440 with 25 off ? 10. $320 with 12^ and 10 off ?
4. $500 with 5 off ? 11. $450 with 33 J and 5 off ?
5. $100 with 2i off ? 12. $800 with 25 and 10 off?
6. $600 with 16f off ? 13. $750 with 20 and 16f off ?
7. $900 with 11^ off? 14. $160 with 37^ and 20 off ?
15. The net price of a bill of goods, subject to 10
off, was $72. 'What was the list price ?
16. The net price of a bill of goods, subject to 25
off, was $180. What was the list price ?
17. A sold C goods billed at $160 and offered a
single discount of 12 J- off, or 10 and 5 off for cash.
How much would C gain by accepting the last offer ?
ilENTAL ABITHMETIC, 179
LeMion 35.
1. If a captain sails a small schooner for f of the
" net stock " ; what do the owners receive from the
proceeds of a voyage that nets $200 ?
Note. The " net stock " is obtained by subtracting all port
charges from the sum received for freight^ other charges are paid
by the owners of the boat.
2. The captain of a small schooner has f of the
"net stock"; what does he receive from a voyage
that nets $78 ?
3. A schooner sailed from Port Liberty to Boston
with 229 tons of coal, on which the freight was $1
per ton ; the port charges were $34 and the vessel's
bills $5 ; if the captain receives J of the " net stock,"
how many dollars do the owners receive ?
4. A schooner sailed from New York to New
London with 200 tons of coal, on which the freight
was 50 cents per ton; the port charges were $16
and the vessel's bills $3 ; the captain sailed the
vessel for ^ of the "net stock"; how many dollars
did the owners receive ?
5. A schooner carried 250 tons of coal from New
York to Dover at $1.10 per ton, the port charges
were $50 and the vessel's bills $10 ; if the captain
sails the vessel for f of the " net stock," how many
dollars do the owners receive ?
6. A captain sailed a certain schooner for f of the
" net stock." This schooner carried 300 tons of coal
from New York to Exeter at $1 per ton; if the
port charges were $55 and the vessel's bills $8,
how many dollars did the owners receive?
180 MENTAL ABITHMETIC.
LesBon 36.
1. A cubic foot of water weighs 1000 ounces. If
a cubic foot of roll sulphur weighs 2000 ounces, how
many times the weight of the water is the weight of
the sulphur ? How many times the weight of any
volume of water will be the weight of a like volume
of roU sulphur ?
2. A cubic foot of water weighs 1 000 ounces, and
a cubic foot of basalt weighs 3000 ounces ; how many
times the weight of the water is the weight of the
basalt ?
3. A cubic foot of water weighs 1000 ounces, and
a cubic foot of clay weighs 1900 ounces ; how many
times the weight of the water is the weight of the clay ?
4. If gold is 19.3 times as heavy as water, an^
a cubic foot of water weighs 1000 ounces, how many
ounces will a cubic foot of gold weigh ?
Note. 19.3 means the same as 19^^^ ; 1.03 means It^.
5. Iron is 7.8 times as heavy as water. If a cubic
foot of water weighs 1000 ounces, how many ounces
will a cubic foot of iron weigh ?
6. Silver is 10.5 times as heavy as water. If a
cubic foot of water weighs 1000 ounces, how many
ounces will two cubic feet of silver weigh ?
7. Hard coal is 1.5 times as heavy as water. If a
cubic foot of water weighs 62^ pounds, how many
pounds will 4 cubic feet of hard coal weigh ?
Note. The number of times the weight of any suhstance
contains the weight of an equal volume of water is called the
specific gravity of the substance.
MENTAL ARITHMETIC. 181
Xaeaaoa 37.
1. The specific gravity of the diamond is 3.6; how
many times the weight of an equal volume of water
is the weight of a diamond ?
2. If the specific gravity of lead is 11.3, and a
cubic foot of water weighs 1000 ounces, how many
ounces will 6 cubic feet of lead weigh ?
3. The specific gravity of mercury is 13.6. A
cubic foot of water weighs 1000 ounces. How many
ounces will ^ a cubic foot of mercury weigh ?
4. The specific gravity of tin is 7.3. A cubic foot
of water weighs 1000* ounces. How many ounces will
J of a cubic foot of tin weigh ?
5. The specific gravity of crown glass is 2,b, and
a cubic foot of water weighs 1000 ounces ; how many
ounces will J of a cubic foot of crown glass weigh ?
6. A cubic foot of brass weighs 8400 ounces, and
a cubic foot of water weighs 1000 ounces ; what is the
specific gravity of brass ?
7. The specific gravity of brick is 2.1 ; if a cubic
foot of water weighs 1000 ounces, how many ounces
will 9 cubic feet of brick weigh ?
8. The specific gravity of chloroform is 1.5. A
vessel contains a mixture of water and chloroform
which weighs 2500 ounces. The volume of the mix-
ture is 2 cubic feet ; what part by volume is chloro-
form, and what part water ? What part by weight
is chloroform, and what part water ?
9. Which is the heavier, a cubic foot of milk,
whose specific gravity is 1.03, or a cubic foot of
glycerine, whose specific gravity is 1.27?
182 MENTAL ARITHMETIC.
38.
1. A and B hired a pasture for $48 ; A pastured
5 cows and B 7 cows ; how much should each pay ?
Solution : If A pastured 5 cows and B 7, they both pastured
5 + 7, or 12 cows. If the pasturage of 12 cows cost $48, the
pasturage of 1 cow would cost ^ of $48, or $4 ; hence the pas-
turage of 5 cows, A*s number, will cost 6 times $4, or $20 ; and
the pasturage of 7 cows, B*s number, will cost $28.
2. James and William bought 36 oranges for 18
cents ; James paid 12 cents and William 6 c^nts ;
how many oranges should each receive ?
3. Two farmers hired a pasture for $75 ; one turns
in 65 cows and the other 100 sheep; how much
should each pay, if a cow eats as much as 10 sheep ?
4. Three men, A, B, and C, bought 120 cords of
wood for $300, of which A paid i, B ^, and C the
remainder ; how many cords did each receive ?
5. Three men, A, B, and C, hired a pasture for
$150; A puts in 25 oxen, B 26 steers, and C, 120
sheep ; how much should each pay, if 2 steers eat
as much as 1 ox, and 5 sheep as much as 1 steer ?
6. A and B agree to do a piece of work for $78 ;
A sends 9 men and B 24 boys ; how much should
each receive, if 3 men "do as much work as 5 boys ?
7. Two partners gain in trade $80 ; A put in $250,
and B $150 ; what is each man's share of the gain?
8. A and B hire a pasture for $38 ; A turns in 6
cows for 3 weeks, and B 10 cows for 2 weeks ; how
much should each pay ?
9. Two partners lose in trade $90 ; A put in $500,
and B $400 ; what is each man's share of the loss ?
MENTAL ARITHMETIC. 183
LeMon 39.
1. If A can do a piece of work in 3 days, and
B in 5 days, what part of it can they both do in 1 day ?
How many days will it take them to do the work ?
Solution : If A can do the work in 3 days, in 1 day he can
do i of the work ; if B can do the work in 5 days, in 1 day he
can do ^ of the work. Hence the part of the work that both A
and B can do in 1 day is | + i, or ^ ; and the number of days
required is H "=" A ~ 1 J days.
2. A can do a piece of work in 4 days, B in 6 days,
and C in 12 days ; how much can they all do in 1 day ?
3. A family uses a barrel of flour in 3 months,
another family uses a barrel in 6 months ; how much
flour will both families use in 1 month ?
4. A man can do a piece of work in 6 days, and
another man can do it in 8 days ; in what time will
they do it working together ?
5. A and B can do a piece of work in 3 days, A
alone in 5 days ; in how many days can B do the work ?
6. A sportsman and his guide together eat 4 pounds
of pork in 3 days. If the sportsman eats 4 pounds in
7 days, how long will the same quantity last the guide ?
7. A cistern has 2 pipes; by the first it can be
emptied in 10 hours, and by the second in ^ of the
time ; how long will both be in emptying it ?
8. A and B can lay a wall in 9 days, A alone in
15 days ; in how many days can B do the work?
9. An open grate and a range consume 1 ton of
coal in H months. If the range consumes 1 ton in
2 months, how much will the grate consume in 2
months ?
184 MEKTAL ARITHMETIC.
1. Three pipes lead from a cistern ; by the first it
can be emptied in 2 hours, by the second in 3 hours,
by the third in 6 hours ; what part of the oistern can
the 3 pipes together empty in 1 hour?
2. If 3 men can dig a ditch in if days^ how many
days will it take 1 man to dig it ?
3. John can cut a cord of wood in f of a day, and
James in | of a day ; in what part of a day can they
together cut a cord?
4. If 9 men can do a piece of work in 7f days,
how long will it take 1 man to do it ?
6. If a man can travel 8} miles in 2 hours, how
many miles can he travel in 5 hours ?
6. A can do a piece of work in 7 hours, and B in
11 hours ; how many hours will it take both to do it?
7. A, B, and C can together make a fence in 9
days ; C alone can make the fence in 36 days ; in
how many days can A and B together make it ?
8. A and B can plow a field in 4 days ; A alone
can plow it in 7 days ; if A and B work 2 days, how
many days will it take A alone to finish the job ?
9. If 5 horses will eat 16|^ loads of hay in a year,
what will 8 horses eat in the same time ?
10. A man did -^ of a piece of work the first day,
^ on the second, and ^ on the third ; how long will
it take another man to finish the piece of work, if he
can do the whole of it in 1 day ?
U. A and B can do a piece of work in 7 days ; C
alone in 20 days ; how many days will it take to
finish the work, if A and B work 3^ days ?
MENTAL ABITHHBTIC. 185
Lesson 41.
1. A man receives his board and ^2 a day for
labor, and pays for board $1 each day he is idle; at
the expiration of 40 days he receives $69 ; how
many days was he idle ?
Solution : Had he labored 40 days, he would have received
40 times $2, or $80 ; he therefore lost $80 — $69, or $21, by
his idleness. Every day he was idle he lost his wages, $2, and
paid for board $1 ; he, therefore, lost $3 every day he was idle.
Hence, to lose $21 it required as many days as there are 3*s
in 21, or 7. Therefore he was idle 7 days.
2. A laborer receives $1.50 a day and boards and
pays for every day he is idle 60 cents for board ; how
many days was he idle, if at the end of 20 days he
received $20 ?
3. John agreed to pick 26 quarts of berries at 2
cents a qt., and to pay 8 cents for every qt. he sold ;
he received 20 cents ; how many quarts did he sell ?
4. A laborer receives $1.76 a day and board, but
pays 26 cents for board for every day he is idle ; at
the end of 12 days he receives $17 ; how many days
does he work ?
5. A boy agreed to carry 60 eggs to market for J of
a cent apiece, and to pay If cents for every egg broken ;
he received 6 cents ; how many eggs .were broken ?
6. Frank agreed to carry 100 peaches to market for
^ a cent each, and to pay 1^ cents for each one he ate ;
he received 40 cents ; how many did he eat?
7. A man receives $2.60 a day for his work, and
pays 60 cents a day for board ; at the end of 30 days
he has saved $48 ; how many days did he work?
186 MENTAL ABITHMETIC.
Zieaaon 42.
1. How far may a person ride in a coach which
goes at the rate of 10 miles an hour so that he may
be gone 7 hours, provided he walks home at the rate
of 4 miles an hour ?
Solution : If he goes 10 miles an hour, he will go 1 mile in
^ of an hour ; and if he returns 4 miles an hour, he will return
1 mile in ^ of an hour ; hence to go and return a mile, it takes
i ~^ 1^0) o^ ^0^ ^^ hour. Hence in 7 hours he can go and
return as many miles as ^ is contained times in 7, or 20 miles.
2. How many miles may a person ride in a coach
going 9 miles an hour, if he is gone 14 hours, and
walks back at the rate of 5 miles an hour ?
3. How many miles may a person sail in a vessel
going 12 miles an hour, if he is gone only 3 hours
and returns at the rate of 6 miles an hour ?
4. If a boat can go 6 miles an hour in still water,
how far up a river that has a current of 2 miles an
hour can it go so as to return in 3 hours ?
5. Suppose that, for every 6 cows a Dutchman has,
he should plow 2 acres of land, and allow 1 acre of
pasture for every 2 cows ; how many cows could be
kept on 25 acres ?
Solution : If for every 6 cows he plows 2 acres, for 1 cow he
plows 1^ of an acre ; and if for every two cows he pastures 1
acre, for 1 cow he pastures ^ of an acre ; hence 1 cow requires
l+j^, or { of an acre, and on 25 acres he could keep as many
cows as I is contained times in 26, or 30 cows.
6. Suppose that, for every 3 cows a Dutchman has,
he should plow 1 acre of land, and allow 1 acre of
pasturage for every 5 cows ; how many cows could
he keep on 24 acres ?
MENTAL ABITHMETIG. 187
LeflMon 43.
Thesmometess. On the scale of the Fahrenheit thermom-
eter, the temperature of meltmg ice is marked 32 degrees, and
of boiling water, 212 degrees ; on the Centigrade thermometer,
the temperature of melting ice is marked degrees, and of boil-
ing water, 100 degrees. There are, then, on the Fahrenheit
scale, 180 degrees from the temperature of melting ice to the
temperature of boiling water ; and on the Centigrade scale 100
degrees from the temperature of melting ice to the temperature
of boiling water. So 180 degrees Fahrenheit corresponds to 100
degrees Centigrade, or 9 degrees Fahrenheit to 6 degrees Centi-
grade.
1. A Fahrenheit thermometer indicates a tempera-
ture of 68 degrees ; what will this temperature be
on the Centigrade scale ?
Solution: As the temperature of melting ice is indicated on
the Fahrenheit scale by 32 degrees, the number of degrees from
this temperature to the temperature given would be 08 — 32,
or 36 degrees ; and this corresponds to f of 36, or 20 degrees
Centigrade.
2. A Fahrenheit thermometer indicates a tempera-
ture of 95 degrees ; what will this temperature be
on the Centigrade scale ?
3. A Fahrenheit thermometer indicates a tempera-
ture of 50 degrees ; what will this temperature be
on the Centigrade scale ?
4. A Centigrade thermometer indicates a tempera-
ture of 20 degrees ; what will this temperature be
on the Fahrenheit scale ?
Answer : f of 20 + 32, or 68 degrees.
5. A Centigrade thermometer indicates 16 de-
grees ; what will this temperature be on the Fahren-
heit scale ?
188 MENTAL ABITHHETIC.
LoMon 44.
1. How many cubic feet will 2 cubic feet of air at
degrees Centigrade occupy when its temperature is
raised 1 degree C? When raised 2 degrees C?
When raised 10 degrees C. ?
Note. A cubic foot of air at degrees, if free to expand
when heated, will increase in volume \fj j\j of a cubic foot on
having its temperature raised 1 degree Centigrade; ^^ of a
cubic foot on having its temperature raised 2 degrees Centigrade.
A cubic foot of air at degrees C. will, if free to do so, contract
by ^f^ of a cubic foot when its temperature is lowered 1 de-
gree C.
2. What volume will a quantity of air that measures
2 cubic feet at degrees C. become when cooled 1 de-
gree C? When cooled 2 degrees C?
3. To what temperature must 1 cubic foot of air
at degrees G. be raised in order that it may occupy
a volume of 2 cubic feet ?
4. If a cubic foot of air at degrees always con-
tracts by ^1^ of a cubic foot for every degree its tem-
perature is diminished, how many degrees must the
air be cooled that it may occupy no assignable space ?
Note. The answer to the last question is called the zero
of temperature on the absolute scale. So low a temperature as
this has not been obtained, and probably long before the air
reached this temperature it would be condensed into a liquid.
5. How many cubic feet would a quantity of air,
which at degrees C. fills a space of 1 cubic foot,
occupy when raised in temperature 100 degrees C?
6. How. many cubic feet would the air mentioned
in the last question occupy if it had been cooled to
100 degrees below ?
lanrrAii abithmeticl 189
IiaBion 45.
X. I bought pears at the rate of 3 for 5 cents, and
sold them at the rate of 4 for 7 cents. What must I
charge for oranges bought at the rate of 3 for a dime
to make the same rate of profit ?
2. I bought lamps at $1.80 a dozen ; f(x what
must I sell them apiece to gain 20 per cent ?
3. I hare put 2 gallons of water into 10 gallons of
vinegar for which I paid 15 cents a gallon. If I sell
the mixture at 16 cents a gallon, what is my gain per
cent of the cost ?
4. What is the cost of 2 bu. 3 pk. 6 qt. of cherries
at 80 cents a pk. ? at f 2.40 a1t)u. ? at 8 cents a qt ?
5. I exchanged a field, 80 rods by 60 rods, for 120
bbl of flour at $5.00 a barrel. What did I receire
per acre for the land ?
6. A and B gained $500. A's stock was $700
and B's $500, and their expenses were $140. What
is each man's share of the net gain ?
7. A man a^eed to saw a cord of wood for $2.50,
catting each stick into 3 pieces. What should I pay
him if I hare him cut each stick into 4 pieces?
8. John writes a letter to his mother four times a
week, and uses three half -sheets of paper for each
letter ; what will his paper for a term of 20 wedu
cost at $6.00 a ream ?
9. In a room, 30 ft. by 20 ft., Uiere are three win-
dows, each 6 ft high and 5 ft. wide. What per cent
of the 4oor surface is the window surface ?
10. The dividend is 113, the quotient 12^ the re-
mainder 5 ; what is the divisor ?
190 MENTAL ABITHMETIC.
Leflson 46.
1. On Monday, I sold f of my pears ; on Tuesday,
I sold 16 more than one-half the remainder, and had
20 pears left. How many had I at first ?
2. The remainder is If, and the subtrahend 3f ;
what is the minuend ?
3. A can do a piece of work in 2 days, and B can
do it in 3 days. After A has worked half a day,
how long will it take B to finish it?
4. After spending \ of my money, I earned half
as much as I had left ; if I then had $13.20, how
much did I spend ?
5. I bought a pile of four-foot wood, but on meas-
uring I found the sticks to be only 3 ft. 8 in. long.
What per cent should be deducted from the price of
the wood ?
6. If the pile of wood in example 5 was 36 feet
long and 4 feet high, and was sold to me at $4.80 a
cord, how much did I save by discovering that the
sticks were 4 inches short ?
7. How many steps, each 2 ft. 6 in., would be
taken in walking along the boundary of a square
that measures 10 rods on a side ?
8. The fence to a rectangular lot that is twice as
long as it is wide is 120 rods in length. How many
acres does the lot contain ?
9. If I mix 3 pounds of 40-cent tea, one pound at
75 cents and one pound at 80 cents, what must I
charge for one pound of the mixture to gain 20^ ?
10. A product is 4^, the multiplier is If ; what is
the multiplicand ?
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